Algebra 2 2-4 More About Linear Equations

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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)

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Problem 1 Got It?

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

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

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Problem 3 Got It?

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F.IF.9

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

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

x-intercept
y-intercept

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F.IF.9

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

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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.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

A.CED.2

F.IF.9

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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.

We have released a new and improved Graphing question type! Students will no longer be able to answer this question.

A.CED.2

F.IF.2

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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?

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F.IF.2

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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?

F.IF.2

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Problem 6 Got It?

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F.IF.9

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Problem 6 Got It?

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F.IF.9

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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.

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

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

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

F.IF.9

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

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

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F.IF.9

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Understanding: If the intercepts of a line are (a, 0) and (0, b), what is the slope of the line?

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

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F.IF.9

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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}

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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}

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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

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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

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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)

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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

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Reflection: Math Success

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F.IF.1

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Algebra 2 2-4 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?

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.

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

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?

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.

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

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

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