Algebra 1 5-4 Complete Lesson: Point-Slope Form - Matt Richardson | Library

Note from the author:

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.

Solve It! The red line shows the altitude of a hot-air balloon during its linear descent. What is an equation of the line in slope-intercept form? Hint: What is the altitude of the balloon when it starts its descent at x = 0?

y = 2x + 650

y = -10x + 640

y = -2x + 650

F.IF.4

F.LE.2

F.LE.5

Problem 1 Got It?

A

B

C

D

F.LE.2

Problem 2 Got It? What is the graph of the equation?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

F.IF.7.a

Problem 3 Got It? In the last step of Problem 3, use the point (-2, -3) instead of (1, 4) to write an equation of the line.

y - 4 = (7/3)(x - 2)

y - 3 = (7/3)(x - 2)

y + 3 = (7/3)(x + 2)

y - 4 = (7/3)(x + 2)

F.LE.2

Problem 3 Got It? Reasoning: Rewrite the equations in Problem 3 and in the previous item in slope-intercept form. Compare the two rewritten equations. What can you conclude?

A.SSE.2

F.BF.3

F.LE.2

Problem 4 Got It? The table shows the number of gallons of water y in a tank after x hours. The relationship is linear. What is an equation in point-slope form that models the data? What does the slope represent?

F.LE.2

F.LE.5

Problem 4 Got It? Reasoning: Rewrite the equation from the previous item in slope-intercept form. What does the y-intercept represent?

A.SSE.2

F.IF.4

F.LE.2

What are the slope and one point on the graph of the equation below?

slope: 4/9; point: (-12, 7)

slope: 4/9; point: (7, 12)

slope: 4/9; point: (-7, 12)

slope: 4/9; point: (12, 7)

What is an equation of the line that passes through the point (3, -8) and has slope -2?

y + 8 = -2(x - 3)

y + 8 = -2(x + 3)

y - 8 = -2(x - 3)

y - 8 = -2(x + 3)

10.

What is an equation of the line that passes through the points (-1, -2) and (2, 4)?

y + 1 = 2(x - 2)

y + 1 = 2(x + 2)

y + 2 = 2(x - 1)

y + 2 = 2(x + 1)

F.LE.2

11.

What is the graph of the equation below?
Be sure to include relevant graph detail: label axes, indicate units on both axes, and use arrows to represent end behavior, as appropriate.

F.IF.7.a

12.

Vocabulary: What features of the graph of the equation below can you identify?

F.LE.2

13.

Reasoning: Does the graph of the equation below include the point (-2, 1)? Explain.

14.

Reasoning: Can any equation in point-slope form also be written in slope-intercept form? Give an example to explain.

A.SSE.2

15.

Review Lesson 5-3: Match the slopes m and y-intercepts b with their equations.

m = 1
m = -1
m = 6
b = 0
b = 4
b = -13

y = x + 4
y = 6x
y = -x - 13

16.

Review Lesson 2-5: Solve the equation for y.

y = 7z/x

y = z/7x

y = 7xz

17.

Review Lesson 2-5: Solve the equation for y.

y = (3b + 7) / a

y = (7b + 3) / a

y = (7b - 3) / a

18.

Review Lesson 2-5: Solve the equation for y.

y = 6c - x

y = -c/6 + x

y = c/6 - x

19.

Vocabulary Review: Classify each equation based on its y-intercept.

y = 3x + 4
y = 4x - 3
y = 5x + 3
y = -3x + 2

Has a y-intercept of 3
Has a y-intercept other than 3

20.

Vocabulary Review: Categorize each equation based on whether or not it is in slope-intercept form.

2x - y = 10
x + 3y + 11 = 0
y - 4 = 2(x + 7)
y = 2x + 6

Slope-intercept form
NOT Slope-intercept form

21.

Vocabulary Review: Classify each statement based on whether or not it is true about the y-intercept of any graph.

occurs where y = 0 on the graph
occurs where x = 0 on the graph
occurs where the graph touches the x-axis

True of the y-intercept of any graph
NOT true of the y-intercept (of at least some graphs)

22.

Use Your Vocabulary: Complete each sentence with the appropriate word from the list.

price
sun
time

The length of a shadow is a function of the angle of the __?__.
The amount of water that has leaked from a leaky faucet is a function of __?__.
The amount of sales tax you pay is a function of the item's __?__.

100

23.

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.