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Point Slope Form - Printable Mathematics Worksheets year 12 - Wayground

Point Slope Form

20 questions

9th - 12th Grade

Mathematics

Point Slope Form is a mathematics worksheet for students in Grades 9–12 who are learning to work with linear equations in point-slope form. Across 20 questions, including 7 fill-in-the-blank items and 13 multiple-choice items, students solve point-slope equations for y and identify the correct algebraic form. The practice reinforces how the slope and coordinate values in a point-slope equation affect the resulting equation. The worksheet also includes graph-based questions that ask students to graph a line and select the point-slope equation represented by a graph, including an item that uses a marked blue point. These questions connect symbolic equations with visual representations and help students check whether a line, slope, and point correspond. This free printable worksheet includes a complete answer key and is suitable for independent practice, review, or a formative check of understanding.

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Worksheets

Point Slope Form

Total questions: 20

Name
Class
Date
1.

Solve for y:

y-5=3(x-4)

(a)  

2.

Solve for y:

y+3=5(x-2)

(a)  

3.

Solve for y:

y-10=-3(x+3)

(a)  

4.

Solve for y:

y-7=3(x+4)

(a)  

5.

Solve for y:

y+8=6(x-10)

(a)  

6.

Solve for y:

y-7=4(x-4)

(a)  

7.

Solve for y:

y+11=-9(x+3)

(a)  

8.

Solve for y

y−4=2(x+3)y-4=2\left(x+3\right)

a)

y=2(x+3)−4y=2\left(x+3\right)-4

b)

y=2(x+3)+4y=2\left(x+3\right)+4

c)

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

d)

y=2(x+3)4y=2\left(x+3\right)4

9.

Solve for y

y+5=13(x−2)y+5=\frac{1}{3}\left(x-2\right)

a)

y=13(x−2)+5y=\frac{1}{3}\left(x-2\right)+5

b)

y=13(x−2)−5y=\frac{1}{3}\left(x-2\right)-5

c)

y=13(x−2)5y=\frac{\frac{1}{3}\left(x-2\right)}{5}

d)

y=13(x−2−5)y=\frac{1}{3}\left(x-2-5\right)

10.

Solve for y

y−5=−4(x+1)y-5=-4\left(x+1\right)

a)

y=−4(x+1)−5y=-4\left(x+1\right)-5

b)

y=−4(x+1)+5y=-4\left(x+1\right)+5

c)

y=−4(x+1)5y=-\frac{4\left(x+1\right)}{5}

d)

y=−4(x+1+5)y=-4\left(x+1+5\right)

11.

Solve for y

y+10=3(x+6)y+10=3\left(x+6\right)

a)

y=3(x+6)+10y=3\left(x+6\right)+10

b)

y=3(x+6)−10y=3\left(x+6\right)-10

c)

y=3(x+6)10y=\frac{3\left(x+6\right)}{10}

d)

y=3(x+6−10)y=3\left(x+6-10\right)

12.

Solve for y

y−9=25(x−8)y-9=\frac{2}{5}\left(x-8\right)

a)

y=25(x−8)−9y=\frac{2}{5}\left(x-8\right)-9

b)

y=25(x−8)+9y=\frac{2}{5}\left(x-8\right)+9

c)

y=25(x−8+9)y=\frac{2}{5}\left(x-8+9\right)

d)

y=25−9(x−8)y=\frac{2}{5}-9\left(x-8\right)

13.

Graph the line:  y+1=−13(x−2)y+1=-\frac{1}{3}(x-2)  

a)
b)
c)
14.

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)

15.

Which point-slope equation matches the graph?

a)

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

b)

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

c)

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

d)

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

16.

What is the point slope form equation for the given line?(Use blue point for formula)

a)

y + 3 = 3 (x + 4)

b)

y + 4 = -3 (x + 3)

c)

y - 4 = 3 (x - 3)

d)

y + 4 = 3 (x + 3)

17.

Which point-slope equation matches the graph?

a)

y−1=−12(x+1)y-1=-\frac{1}{2}\left(x+1\right)  

b)

y+1=−12(x−1)y+1=-\frac{1}{2}\left(x-1\right)  

c)

y−1=−2(x+1)y-1=-2\left(x+1\right)  

d)

y+1=−2(x−1)y+1=-2\left(x-1\right)  

18.

Graph the equation: y + 1 = 3 (x – 2)

a)
b)
c)
d)
19.

Graph the equation: y – 3 = –2(x + 4)

a)
b)
c)
d)
20.

Graph the equation: y – 4 = –1(x + 2)

a)
b)
c)
d)
Answer Key

Point Slope Form

Total questions: 20

1.
y=3(x-4)+5
2.
y=5(x-2)-3
3.
y=-3(x+3)+10
4.
y=3(x+4)+7
5.
y=6(x-10)-8
6.
y=4(x-4)+7
7.
y=-9(x+3)-11
8.
b)

y=2(x+3)+4y=2\left(x+3\right)+4

9.
b)

y=13(x−2)−5y=\frac{1}{3}\left(x-2\right)-5

10.
b)

y=−4(x+1)+5y=-4\left(x+1\right)+5

11.
b)

y=3(x+6)−10y=3\left(x+6\right)-10

12.
b)

y=25(x−8)+9y=\frac{2}{5}\left(x-8\right)+9

13.
a)
14.
a)

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

15.
b)

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

16.
d)

y + 4 = 3 (x + 3)

17.
d)

y+1=−2(x−1)y+1=-2\left(x-1\right)  

18.
b)
19.
d)
20.
b)

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FAQs

What does this Point Slope Form worksheet help students learn?

This worksheet helps Grades 9–12 students solve point-slope equations for y and connect those equations to linear graphs. Its 7 fill-in-the-blank problems focus on rearranging equations such as y − 5 = 3(x − 4), while the 13 multiple-choice questions include solving for y, graphing a line, and identifying the point-slope equation that matches a graph and its marked point.

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

Introduce the worksheet by reviewing how to isolate y while preserving the slope and the sign of the constant term. Model one fill-in-the-blank equation, then have students explain each algebraic step before moving to the multiple-choice graph items. For the graph questions, ask students to identify the marked point and slope first, then use those features to justify the matching point-slope equation.

What mistakes should I watch for when students complete this worksheet?

Students may change the sign incorrectly when moving a constant across the equal sign, such as treating y + 3 = 5(x − 2) as though the constant were added to y after solving. In the graph items, watch for reversed signs in expressions such as x + 2 versus x − 2, choosing the wrong slope sign, or using a point that is not the marked blue point. Students may also select an equation that looks similar without checking it against the graph.

How do I assign and grade this Point Slope Form worksheet?

Wayground provides this worksheet as a printable PDF and as a digital quiz, so you can use the fill-in-the-blank and multiple-choice questions in the format that fits your lesson. It includes a complete answer key for grading the 20 responses, and printable submissions can be graded by scanning student work with the Wayground for Teachers app. The printable version can also support classes that are reducing screen time.

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

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the algebraic expressions and graph prompts are easier to read. You can also select a dyslexia-friendly font or translate the worksheet’s directions and text into another language while students work through the point-slope equations and graph-matching items.

Where can I find more worksheets like this on Wayground?

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

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