Algebra 2 2-4 Guided Practice: More About Linear Equations

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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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.

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

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

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Provide an example of an equation written in point-slope form.

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Take Note: Explain why it is appropriate to find the words "point" and "slope" in the name point-slope form.

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Problem 1 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

Review: The slope formula helps us to calculate the slope between any two points as follows:
\frac{y_{2}-y_{1}}{x_{2}-x_{1}}

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Take Note: Describe the process of using the slope formula to calculate slope between two given points.

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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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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Provide an example of an equation in standard form.

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Take Note: Since the standard form of an equation should be written with integers as its coefficients and constant, it is often necessary to clear fractions. Recall that this can be accomplished by multiplying every term in the equation by the least common multiple (LCM) of all of the denominators.

Consider the equation:
\frac{2}{3}x+5y=\frac{1}{2}
By what LCM can we multiply every term to clear the fractions and establish an equation that is in standard form? Enter only a number.

Hint: The new equation is
4x+30y=3.

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Problem 3 Got It?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Classify each item on the left based on the form of an equation that it represents.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

y=\frac{2}{3}x-5
y-2=-3(x-4)
Ax+By=C
y=mx+b
y-y_{1}=m(x-x_{1})
7x-6y=1

Slope-Intercept Form
Point-Slope Form
Standard Form

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

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

x-intercept
y-intercept

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Problem 4 Got It? Graph the equation 2x - 4y = 8.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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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 knows that the paper will last about 80 days.

What graph represents this situation? Zoom and pan your graph to establish an appropriate viewing window.

Tip: Zoom out until you can see 140 on the y-axis and 80 on the x-axis.

Instructions

Click the graph tab.
Click on the graph background to add a point. Add two points to create a graph. Drag a point or type in x and y coordinates to edit its position. Click on a point to delete it.

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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 knows that the paper will last about 80 days.

What is the equation of the line in standard form?

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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 knows that the paper will last about 80 days.

How many packs of printer paper should the manager expect to have after 30 days?

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Video Check: Select all that apply with regards to the video embedded directly above this item.

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Take Note: Describe what you know about the slopes of parallel lines.

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Problem 6 Got It?

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Problem 6 Got It?

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Algebra 2 2-4 Guided Practice: More About Linear Equations

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Provide an example of an equation written in point-slope form.

Take Note: Explain why it is appropriate to find the words "point" and "slope" in the name point-slope form.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Describe the process of using the slope formula to calculate slope between two given points.

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)?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Provide an example of an equation in standard form.

Problem 3 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Classify each item on the left based on the form of an equation that it represents.You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

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

Problem 4 Got It? Graph the equation 2x - 4y = 8.

Video Check: Select all that apply with regards to the video embedded directly above 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 knows 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 knows that the paper will last about 80 days. How many packs of printer paper should the manager expect to have after 30 days?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Describe what you know about the slopes of parallel lines.

Problem 6 Got It?

Problem 6 Got It?

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Provide an example of an equation written in point-slope form.

Take Note: Explain why it is appropriate to find the words "point" and "slope" in the name point-slope form.

Problem 1 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Describe the process of using the slope formula to calculate slope between two given points.

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)?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Provide an example of an equation in standard form.

Problem 3 Got It?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Classify each item on the left based on the form of an equation that it represents.You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

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

Problem 4 Got It? Graph the equation 2x - 4y = 8.

Video Check: Select all that apply with regards to the video embedded directly above 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 knows 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 knows that the paper will last about 80 days. How many packs of printer paper should the manager expect to have after 30 days?

Video Check: Select all that apply with regards to the video embedded directly above this item.

Take Note: Describe what you know about the slopes of parallel lines.

Take Note: What is the slope of a line that is parallel to the line given by the equation y=-4x? Enter only a number.

Take Note: Define negative reciprocal.

Take Note: Provide an example pair of two numbers that are negative reciprocals.

Take Note: Describe what you know about the slopes of perpendicular lines. You may use the canvas to help illustrate your written description.

Take Note: What is the slope of a line that is perpendicular to the line given by the equation y=-4x? Enter only a number.

Problem 6 Got It?

Problem 6 Got It?

🧠 Retrieval Practice:Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: What is the slope of a line that is parallel to the line given by the equation y=-4x? Enter only a number.

Take Note: Define negative reciprocal.

Take Note: Provide an example pair of two numbers that are negative reciprocals.

Take Note: Describe what you know about the slopes of perpendicular lines. You may use the canvas to help illustrate your written description.

Take Note: What is the slope of a line that is perpendicular to the line given by the equation y=-4x? Enter only a number.

Take Note: Classify each item on the left based on the form of an equation that it represents.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows 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 knows that the paper will last about 80 days.

How many packs of printer paper should the manager expect to have after 30 days?

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: Classify each item on the left based on the form of an equation that it represents.

You may need to zoom out to see all of the items. You can also place each item from the left column by selecting it (click it) then selecting (clicking on) the category for it.

Problem 5 Got It? The office manager of a small office ordered 140 packs of printer paper. Based on average daily use, she knows 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 knows that the paper will last about 80 days.

How many packs of printer paper should the manager expect to have after 30 days?

Take Note: What is the slope of a line that is parallel to the line given by the equation y=-4x?
Enter only a number.

Take Note: What is the slope of a line that is perpendicular to the line given by the equation y=-4x?
Enter only a number.

🧠 Retrieval Practice:
Summarize the mathematical content of this lesson. What topics, ideas, and vocabulary were introduced?

Take Note: What is the slope of a line that is parallel to the line given by the equation y=-4x?
Enter only a number.

Take Note: What is the slope of a line that is perpendicular to the line given by the equation y=-4x?
Enter only a number.