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Graphing from Point Slope Form - Printable Mathematics Worksheets year 10 - Wayground

Graphing from Point Slope Form

20 questions

9th Grade

Mathematics

Graphing from Point Slope Form is a Grade 9 mathematics worksheet that helps students recognize, interpret, write, and graph linear equations in point-slope form, y − y₁ = m(x − x₁). Students identify equations in point-slope form, select all valid examples, identify the given point and slope, write an equation from a point and slope, and match equations to graphs. The 20-question set combines 17 multiple-choice items, 2 multiple-select items, and 1 graphing task. Students apply the point-slope structure to move from an equation to a graph and from a graph or given coordinates to an equation, including using slope to plot additional points. This free printable worksheet includes a complete answer key and is designed for Grade 9 math practice, independent work, review, or assessment.

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Graphing from Point Slope Form

Total questions: 20

Name
Class
Date
1.

Which of these represents point-slope form of a linear equation?

a)

y - y1 = m(x - x1)

b)

Ax + By = C

c)

y = mx + b

2.

Select all of the following equations in point-slope form.

a)

y - 2 = 5(x - 2)

b)

3x + 2y = 12

c)

y + 2 = 1/4(x + 4)

d)

y = 4x + 6

e)

2y = 5x - 7

3.

Explain how to graph the following equation... y - 2 = 1/3(x - 3)

a)

Plot the point (−3,−2), move up 1 and right 3 units from there.

b)

Plot the point (3,2), move up 1 and left 3 units from there.

c)

Plot the point (3,2), move up 1 and right 3 units from there.

d)

Plot the point (2,3), move up 1 and right 3 units from there.

4.

Which equation in point-slope form matches the given graph?

a)

y−4=−23(x−1)y-4=-\frac{2}{3}\left(x-1\right)

b)

y+4=−23(x+1)y+4=-\frac{2}{3}\left(x+1\right)

c)

y−4=−32(x−1)y-4=\frac{-3}{2}\left(x-1\right)

d)

y+4=32(x−1)y+4=\frac{3}{2}\left(x-1\right)

5.

Which equation in point-slope form matches the given graph?

a)

y−4=23(x+1)y-4=\frac{2}{3}\left(x+1\right)

b)

y+4=23(x+1)y+4=\frac{2}{3}\left(x+1\right)

c)

y−4=23(x−1)y-4=\frac{2}{3}\left(x-1\right)

d)

y+4=23(x−1)y+4=\frac{2}{3}\left(x-1\right)

6.

Which equation in point-slope form matches the given graph?

a)

y−4=−23(x−1)y-4=-\frac{2}{3}\left(x-1\right)

b)

y+4=−23(x+1)y+4=-\frac{2}{3}\left(x+1\right)

c)

y−4=−32(x−1)y-4=\frac{-3}{2}\left(x-1\right)

d)

y+4=32(x−1)y+4=\frac{3}{2}\left(x-1\right)

7.

Which equation in point-slope form matches the given graph?

a)

y−4=23(x+1)y-4=\frac{2}{3}\left(x+1\right)

b)

y+4=23(x+1)y+4=\frac{2}{3}\left(x+1\right)

c)

y−4=23(x−1)y-4=\frac{2}{3}\left(x-1\right)

d)

y+4=23(x−1)y+4=\frac{2}{3}\left(x-1\right)

8.

Given the point (3, -2) and a slope of 4, what is the equation of the line?

a)

y = 4x + 10

b)

y = -4x - 14

c)

y = 4x - 14

d)

y = -4x + 14


9.

Write the Equation in POINT SLOPE Form


Point (1, -3) m = -2

a)

y - 3 = -2(x + 1)

b)

y + 3 = -2(x - 1)

c)

y - 1 = 2(x +3)

d)

y + 1 = -2(x - 3)

10.

What is the point slope form equation of the graph given(use blue point in equation)

a)

y + 2 = 32\frac{3}{2} (x + 2)

b)

y - 2 = 32\frac{3}{2} (x - 2)

c)

y + 2 = - 32\frac{3}{2} (x + 2)

d)

y - 2= - 32\frac{3}{2} (x - 2)

11.

Graph the line: y + 5 = -4 (x - 8)

12.

For the equation
y - 3 = 2(x + 4),
the line has a slope of 2 and contains what point?

a)

(-4, 3)

b)

(3, -4)

c)

(-3, -4)

d)

(-4, -3)

13.

For the equation
y - 3 = 2(x + 4),
which of the following is true?

a)

The line has m = 2 passing through the point (4, -3)

b)

The line has m = 2 passing through the point (3, -4)

c)

The line has m = 2 passing through the point (-4, 3)

d)

The line has m = 2 passing through the point (-3, 4)

14.

Determine the equation of the line.

a)

y=4x+3y=4x+3

b)

y=3x+4y=3x+4

c)

y=−4x−1y=-4x-1

d)

y=−3x−1y=-3x-1

15.

Determine the equation of the line.

a)

y=32xy=\frac{3}{2}x

b)

y=23xy=\frac{2}{3}x

c)

y=−32y=-\frac{3}{2}

d)

y=23y=\frac{2}{3}

16.

What type of slope does the following graph have?

a)

Postive

b)

Negative

c)

Zero Slope

d)

Undefined

17.

How would you graph a line that has the same slope as Line B and starts at (0, -3)?

a)

Plot the first point at (0, -3); next, go UP 2 : RIGHT 1 and plot the next point.

b)

Plot the first point at (0, -3); next, go DOWN 1 : RIGHT 2 and plot the next point.

c)

Plot the first point at (-3, 0); next, go UP 2 : RIGHT 1 and plot the next point.

d)

Plot the first point at (-3, 0); next, go DOWN 2 : RIGHT 1 and plot the next point.

18.

When graphing the equation y= 1/4x + 2 , after starting at the y-intercept, how do you find your next point?

a)

RISE/RUN

b)

RUN/RISE

c)

Going up 1 and over 4

d)

Going up 4 and over 1

19.

Find the slope of the line.

a)

1/2

b)

-1/2

c)

2

d)

-2

20.

Find the slope.

a)

-5/3

b)

-3/5

c)

5/3

d)

3/5

Answer Key

Graphing from Point Slope Form

Total questions: 20

1.
a)

y - y1 = m(x - x1)

2.
c)

y + 2 = 1/4(x + 4)

, a)

y - 2 = 5(x - 2)

3.
c)

Plot the point (3,2), move up 1 and right 3 units from there.

4.
b)

y+4=−23(x+1)y+4=-\frac{2}{3}\left(x+1\right)

5.
c)

y−4=23(x−1)y-4=\frac{2}{3}\left(x-1\right)

6.
d)

y+4=32(x−1)y+4=\frac{3}{2}\left(x-1\right)

7.
a)

y−4=23(x+1)y-4=\frac{2}{3}\left(x+1\right)

8.
c)

y = 4x - 14

9.
b)

y + 3 = -2(x - 1)

10.
a)

y + 2 = 32\frac{3}{2} (x + 2)

11.
12.
a)

(-4, 3)

13.
c)

The line has m = 2 passing through the point (-4, 3)

14.
a)

y=4x+3y=4x+3

15.
a)

y=32xy=\frac{3}{2}x

16.
b)

Negative

17.
a)

Plot the first point at (0, -3); next, go UP 2 : RIGHT 1 and plot the next point.

18.
a)

RISE/RUN

, c)

Going up 1 and over 4

19.
a)

1/2

20.
a)

-5/3

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FAQs

What does the Graphing from Point Slope Form worksheet cover?

This Grade 9 worksheet focuses on recognizing point-slope form, identifying a line’s slope and given point, writing equations from coordinates or graphs, and graphing a line from its equation. Its 20 items use multiple-choice, multiple-select, and graphing formats so students practice both interpreting the structure y − y₁ = m(x − x₁) and applying it to coordinate graphs.

How can I use this worksheet to teach graphing from point-slope form?

Introduce the form by having students identify the coordinates represented by (x₁, y₁) and the slope represented by m, then model how to plot the given point and use the slope as a rise-over-run pattern. Use the equation-to-graph and graph-to-equation items to prompt students to explain which point and slope they used before completing the independent graphing task.

What mistakes should I watch for when students complete this point-slope form worksheet?

Watch for students reversing the signs in the coordinate point, such as reading x + 4 as an x-coordinate of 4 instead of −4, or changing y − y₁ incorrectly when substituting a negative y-coordinate. Students may also plot the starting point incorrectly, use the slope in the wrong direction, or select only one valid equation on the multiple-select item instead of identifying every equation written in point-slope form.

How do I assign and grade this point-slope form worksheet?

The worksheet is available as a printable PDF and as a digital quiz on Wayground, with a complete answer key for the 17 multiple-choice, 2 multiple-select, and 1 graphing questions. Printable submissions can be graded by scanning student work with the Wayground for Teachers app, while the digital version supports assignment and grading through Wayground.

How can I differentiate this point-slope form worksheet for my students?

In the worksheet’s Advanced Settings, adjust font spacing and font size to make the equation choices, coordinate pairs, and graphing prompt easier to read. You can also enable a dyslexia-friendly font or translate the worksheet into another language when those options support students working with the point-slope examples and graphing directions.

Where can I find more free worksheets like this on Wayground?

Wayground offers a comprehensive collection of free printable worksheets and practice problems across all subjects, with downloadable PDFs and answer keys to help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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