Algebra 2 2-4 Complete Lesson: More About Linear Equations

Last updated over 4 years ago

36 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

A complete formative lesson with embedded slideshow, mini lecture screencasts, checks for understanding, practice items, mixed review, and reflection. I create these assignments to supplement each lesson of Pearson's Common Core Edition Algebra 1, Algebra 2, and Geometry courses. See also mathquest.net and twitter.com/mathquestEDU.

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.2

A.CED.2

F.IF.2

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.9

F.IF.1

F.IF.9

100

A.CED.2

F.IF.1

F.IF.9

Algebra 2 2-4 Complete Lesson: More About Linear Equations

Last updated over 4 years ago

36 Nsɛmmisa

Hyɛ no nsow a efi ɔkyerɛwfo no hɔ:

Solve It! A contractor needs to build two straight roads, each passing through point A. One road must be parallel to Pine Street, and the other road must be perpendicular to Pine Street. Find the coordinates of a second point the parallel road will pass through and the coordinates of a third point the perpendicular road will pass through. Classify the coordinates below appropriately.

(10, 70)
(50, 40)
(60, 60)

On the parallel road
On the perpendicular road
On neither the parallel nor perpendicular road

A.CED.2

Problem 1 Got It?

A.CED.2

F.IF.9

Problem 2 Got It? A line passes through (-5, 0) and (0, 7). What is an equation of the line in point-slope form?

A.CED.2

F.IF.9

Problem 2 Got It? Reasoning: What is another equation in point-slope form of the line through the points (-5, 0) and (0, 7)?

A.CED.2

F.IF.9

Problem 3 Got It?

A.CED.2

F.IF.9

Problem 4 Got It? What are the intercepts of 2x - 4y = 8?

(0, 0)
(4, 0)
(0, -2)
(-4, 0)

x-intercept
y-intercept

A.CED.2

F.IF.9

Problem 4 Got It? Graph the equation 2x - 4y = 8 on the canvas. Use a color other than black.

A.CED.2

F.IF.9

Problem 4 Got It? Graph the equation. Zoom and pan your graph to leave an appropriate scale and viewing window.
You may edit your own graph on the previous item after completing this item.

Yɛayi Graphing asɛmmisa type foforo a wɔatu mpɔn adi! Asuafo rentumi mmua saa asɛmmisa yi bio.

A.CED.2

F.IF.9

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
What graph represents this situation? Zoom and pan your graph to leave an appropriate scale and viewing window.

Yɛayi Graphing asɛmmisa type foforo a wɔatu mpɔn adi! Asuafo rentumi mmua saa asɛmmisa yi bio.

A.CED.2

F.IF.2

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
What is the equation of the line in standard form?

7x + 80y = 560

4y - 7x = 560

7x + 4y = 560

A.CED.2

F.IF.2

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
How many packs of printer paper should the manager expect to have after 30 days?

37 packs

87.5 packs

31.5 packs

19 packs

F.IF.2

Problem 6 Got It?

A.CED.2

F.IF.9

Problem 6 Got It?

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.9

Graphing: What are the intercepts of 3x + y = 6? Graph the equation. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

A.CED.2

F.IF.9

A.CED.2

F.IF.9

A.CED.2

F.IF.9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y + 2 = -2(x - 1)

point-slope form

standard form

slope-intercept form

F.IF.9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y = -¼x + 9

slope-intercept form

standard form

point-slope form

F.IF.9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
-x - 2y = 1

point-slope form

slope-intercept form

standard form

F.IF.9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y - 3 = 4x

point-slope form

slope-intercept form

standard form

F.IF.9

Understanding: Which form would you use to write the equation of a line if you knew its slope and x-intercept? Explain.

A.CED.2

F.IF.9

Understanding: If the intercepts of a line are (a, 0) and (0, b), what is the slope of the line? Assume that a and b are both greater than 0.
Enter only the slope, in simplified fraction form.

A.CED.2

F.IF.9

Error Analysis: Your friend says the line y = -2x + 3 is perpendicular to the line x + 2y = 8. Do you agree? Explain.

Yes; After converting the second equation to slope-intercept form, we can see that its slope is 1/2. Since -2 and 1/2 are opposite reciprocals, the lines are perpendicular.

No; After converting the second equation to slope-intercept form, we can see that its slope is -1/2. Since -2 and -1/2 are not opposite reciprocals, the lines are not perpendicular.

A.CED.2

F.IF.9

Review Lesson 2-1: Match each relation with its domain.

{(-3, 4), (-1, 2), (0, -2), (1, 0), (2, 2)}

Domain: all real numbers
Domain: {-3, -1, 0, 1, 2}
Domain: {-18, -2, 0, 3, 39}

F.IF.1

Review Lesson 2-1: Match each relation with its range.

{(-3, 4), (-1, 2), (0, -2), (1, 0), (2, 2)}

Range: {-2}
Range: {-1, 3, 17, 28, 32}
Range: {-2, 0, 2, 4}

F.IF.1

Review Lesson 2-1: Determine whether each relation represents a function.

{(-3, 4), (-1, 2), (0, -2), (1, 0), (2, 2)}

Function
Not a function

F.IF.1

Review Lesson 1-2: Match each equation with the property of real numbers it illustrates.

Distributive property
Inverse property of multiplication
Inverse property of addition

Review Lesson 2-3: Match the equation of each line in slope-intercept form with its corresponding details on the right.

m = 3 and the y-intercept is (0, -5)
m = 1/2 and the y-intercept is (0, 0)
m = -3/8 and the y-intercept is (0, 3)

F.IF.9

Vocabulary Review: Write the sentence below as an equation.
The sum of x and y is 8.

Vocabulary Review: Write the sentence below as an equation.
The product of p and q is 7.

Vocabulary Review: Write the sentence below as an equation.
The square root of y is x cubed.

Use Your Vocabulary: Use the graph below to categorize each statement as True or False.

The x-intercept of the line is (4, 0).
The x-intercept of the line is (0, 4).
The y-intercept of the line is (-1, 0).
The y-intercept of the line is (0, -1).

True
False

100

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

A.CED.2

F.IF.1

F.IF.9

Algebra 2 2-4 Complete Lesson: More About Linear Equations

Algebra 2 2-4 Complete Lesson: More About Linear Equations

Problem 1 Got It?

Problem 2 Got It? A line passes through (-5, 0) and (0, 7). What is an equation of the line in point-slope form?

Problem 2 Got It? Reasoning: What is another equation in point-slope form of the line through the points (-5, 0) and (0, 7)?

Problem 3 Got It?

Problem 4 Got It? What are the intercepts of 2x - 4y = 8?

Problem 4 Got It? Graph the equation 2x - 4y = 8 on the canvas. Use a color other than black.

Problem 4 Got It? Graph the equation. Zoom and pan your graph to leave an appropriate scale and viewing window. You may edit your own graph on the previous item after completing this item.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days. What graph represents this situation? Zoom and pan your graph to leave an appropriate scale and viewing window.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days. What is the equation of the line in standard form?

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days. How many packs of printer paper should the manager expect to have after 30 days?

Problem 6 Got It?

Problem 6 Got It?

Graphing: What are the intercepts of 3x + y = 6? Graph the equation. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. y + 2 = -2(x - 1)

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. y = -¼x + 9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. -x - 2y = 1

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. y - 3 = 4x

Understanding: Which form would you use to write the equation of a line if you knew its slope and x-intercept? Explain.

Understanding: If the intercepts of a line are (a, 0) and (0, b), what is the slope of the line? Assume that a and b are both greater than 0. Enter only the slope, in simplified fraction form.

Error Analysis: Your friend says the line y = -2x + 3 is perpendicular to the line x + 2y = 8. Do you agree? Explain.

Review Lesson 2-1: Match each relation with its domain.

Review Lesson 2-1: Match each relation with its range.

Review Lesson 2-1: Determine whether each relation represents a function.

Review Lesson 1-2: Match each equation with the property of real numbers it illustrates.

Review Lesson 2-3: Match the equation of each line in slope-intercept form with its corresponding details on the right.

Vocabulary Review: Write the sentence below as an equation.The sum of x and y is 8.

Vocabulary Review: Write the sentence below as an equation.The product of p and q is 7.

Vocabulary Review: Write the sentence below as an equation.The square root of y is x cubed.

Use Your Vocabulary: Use the graph below to categorize each statement as True or False.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 1 Got It?

Problem 2 Got It? A line passes through (-5, 0) and (0, 7). What is an equation of the line in point-slope form?

Problem 2 Got It? Reasoning: What is another equation in point-slope form of the line through the points (-5, 0) and (0, 7)?

Problem 3 Got It?

Problem 4 Got It? What are the intercepts of 2x - 4y = 8?

Problem 4 Got It? Graph the equation 2x - 4y = 8 on the canvas. Use a color other than black.

Problem 4 Got It? Graph the equation. Zoom and pan your graph to leave an appropriate scale and viewing window. You may edit your own graph on the previous item after completing this item.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days. What graph represents this situation? Zoom and pan your graph to leave an appropriate scale and viewing window.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days. What is the equation of the line in standard form?

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days. How many packs of printer paper should the manager expect to have after 30 days?

Problem 6 Got It?

Problem 6 Got It?

Graphing: What are the intercepts of 3x + y = 6? Graph the equation. Be sure to include relevant graph detail: label axes, indicate units and scale on both axes, and use arrows to represent end behavior, as appropriate.

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. y + 2 = -2(x - 1)

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. y = -¼x + 9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. -x - 2y = 1

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form. y - 3 = 4x

Understanding: Which form would you use to write the equation of a line if you knew its slope and x-intercept? Explain.

Understanding: If the intercepts of a line are (a, 0) and (0, b), what is the slope of the line? Assume that a and b are both greater than 0. Enter only the slope, in simplified fraction form.

Error Analysis: Your friend says the line y = -2x + 3 is perpendicular to the line x + 2y = 8. Do you agree? Explain.

Review Lesson 2-1: Match each relation with its domain.

Review Lesson 2-1: Match each relation with its range.

Review Lesson 2-1: Determine whether each relation represents a function.

Review Lesson 1-2: Match each equation with the property of real numbers it illustrates.

Review Lesson 2-3: Match the equation of each line in slope-intercept form with its corresponding details on the right.

Vocabulary Review: Write the sentence below as an equation.The sum of x and y is 8.

Vocabulary Review: Write the sentence below as an equation.The product of p and q is 7.

Vocabulary Review: Write the sentence below as an equation.The square root of y is x cubed.

Use Your Vocabulary: Use the graph below to categorize each statement as True or False.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.For a refresher on the Cornell note-taking system, click here.

Reflection: Math Success

Problem 4 Got It? Graph the equation. Zoom and pan your graph to leave an appropriate scale and viewing window.
You may edit your own graph on the previous item after completing this item.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
What graph represents this situation? Zoom and pan your graph to leave an appropriate scale and viewing window.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
What is the equation of the line in standard form?

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
How many packs of printer paper should the manager expect to have after 30 days?

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y + 2 = -2(x - 1)

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y = -¼x + 9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
-x - 2y = 1

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y - 3 = 4x

Understanding: If the intercepts of a line are (a, 0) and (0, b), what is the slope of the line? Assume that a and b are both greater than 0.
Enter only the slope, in simplified fraction form.

Vocabulary Review: Write the sentence below as an equation.
The sum of x and y is 8.

Vocabulary Review: Write the sentence below as an equation.
The product of p and q is 7.

Vocabulary Review: Write the sentence below as an equation.
The square root of y is x cubed.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.

Problem 4 Got It? Graph the equation. Zoom and pan your graph to leave an appropriate scale and viewing window.
You may edit your own graph on the previous item after completing this item.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
What graph represents this situation? Zoom and pan your graph to leave an appropriate scale and viewing window.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
What is the equation of the line in standard form?

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she know that the paper will last about 80 days.
How many packs of printer paper should the manager expect to have after 30 days?

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y + 2 = -2(x - 1)

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y = -¼x + 9

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
-x - 2y = 1

Vocabulary: Tell whether the equation is in slope-intercept, point-slope, or standard form.
y - 3 = 4x

Understanding: If the intercepts of a line are (a, 0) and (0, b), what is the slope of the line? Assume that a and b are both greater than 0.
Enter only the slope, in simplified fraction form.

Vocabulary Review: Write the sentence below as an equation.
The sum of x and y is 8.

Vocabulary Review: Write the sentence below as an equation.
The product of p and q is 7.

Vocabulary Review: Write the sentence below as an equation.
The square root of y is x cubed.

Notes: Take a clear picture or screenshot of your Cornell notes for this lesson. Upload it to the canvas. Zoom and pan as needed.
For a refresher on the Cornell note-taking system, click here.