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211 - Write Equation Given Two Points - Printable Mathematics Worksheets - Wayground

211 - Write Equation Given Two Points

8 questions

9th - 9th Grade

Mathematics

211 - Write Equation Given Two Points is a free printable Grade 9 mathematics worksheet that builds fluency with slope-intercept form. Across eight multiple-choice questions, students identify the slope formula, interpret m as slope and b as the y-intercept, and read slope and y-intercept values from equations such as y = −⅓x + 1. Students then select slope-intercept equations from a given slope and y-intercept and determine equations for lines passing through two coordinate points. The paired-point items require students to calculate slope, identify the y-intercept, and choose the equation that matches both values. This focused practice helps students connect coordinate information to the form y = mx + b while reinforcing positive and negative signs and fractional slopes. The worksheet is available as a free printable PDF with a complete answer key, making it useful for guided practice, independent review, or a short formative assessment.

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Worksheets

211 - Write Equation Given Two Points

Total questions: 8

Name
Class
Date
1.

What formula can be used to find the slope of a line?

a)

m= y2−y1 x2−x1m=\frac{\ y_2-y_1\ }{x_2-x_1}

b)

y=mx+by=mx+b

c)

Ax+By=CAx+By=C

d)

m= x2−x1 y2−y1m=\frac{\ x_2-x_1\ }{y_2-y_1}

2.

Which statement best describes "m"?

a)

x- intercept

b)

y - intercept

c)

slope

d)

tasty

3.
What does 'b" represent in y=mx=b
a)
y-intercept
b)
beans
c)
nothing
d)
slope
4.

Identify the slope and y intercept to write an equation of the line:  y=−13x+1y=-\frac{1}{3}x+1  

a)

Slope:  13\frac{1}{3}  
y-intercept: 1

b)

Slope:  13\frac{1}{3}  
y-intercept: -1

c)

Slope:  −13-\frac{1}{3}  
y-intercept: 1

d)

Slope:  -\frac{1}{3}  
y-intercept: 0

5.

Write an equation of the line in slope-intercept form:

a)

 y=32x−3y=\frac{3}{2}x-3  

b)

 y=6x+3y=6x+3  

c)

 y=32x+3y=\frac{3}{2}x+3  

d)

 y=4x−3y=4x-3  

6.

Write an equation for the line that passes through the given points:
 (−3, 5)\left(-3,\ 5\right)  and  (0, −1)\left(0,\ -1\right)  

a)

 y=−2x−1y=-2x-1  

b)

 y=−12x−1y=-\frac{1}{2}x-1 

c)

 y=−1y=-1  

d)

 y=−3x+5y=-3x+5  

7.

Write an equation for the line that passes through the given points:
 (0, −2)\left(0,\ -2\right)  and  (4, 10)\left(4,\ 10\right)  

a)

 y=13x−2y=\frac{1}{3}x-2  

b)

 y=3x−2y=3x-2 

c)

 y=4x+10y=4x+10  

d)

 y=2x−2y=2x-2  

8.

Write an equation for the line that passes through the given points:
 (3, 1)\left(3,\ 1\right)  and  (0, 10)\left(0,\ 10\right)  

a)

 y=−3x+10y=-3x+10  

b)

 y=−13x+10y=-\frac{1}{3}x+10 

c)

 y=3x+1y=3x+1 

d)

 y=10y=10  

Answer Key

211 - Write Equation Given Two Points

Total questions: 8

1.
a)

m= y2−y1 x2−x1m=\frac{\ y_2-y_1\ }{x_2-x_1}

2.
c)

slope

3.
a) y-intercept
4.
c)

Slope:  −13-\frac{1}{3}  
y-intercept: 1

5.
a)

 y=32x−3y=\frac{3}{2}x-3  

6.
a)

 y=−2x−1y=-2x-1  

7.
b)

 y=3x−2y=3x-2 

8.
a)

 y=−3x+10y=-3x+10  

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FAQs

What does this worksheet cover, and how does it help students write equations from two points?

This Grade 9 worksheet uses eight multiple-choice questions to develop the skill of writing linear equations in slope-intercept form, y = mx + b. Students identify the slope formula, distinguish m from b, read slope and y-intercept values, and select equations for lines through coordinate pairs. These steps connect two points to the correct slope, y-intercept, and final equation.

How can I use this worksheet to teach writing a line equation from two points?

First model how to calculate m = (y₂ − y₁) ÷ (x₂ − x₁), then show how a point with x = 0 reveals the y-intercept when available. Use the worksheet’s equation-identification items to review m and b before discussing the paired-point questions. Ask students to verify each choice by checking its slope and substituting one of the given points into the equation.

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

Watch for students reversing the slope differences, confusing m with the y-intercept b, or changing the sign of a negative slope or intercept. In the paired-point items, students may choose an equation with the correct slope but the wrong y-intercept, or stop after calculating slope without checking both points. Have students compare each option with the given coordinates to catch these errors.

How do I assign and grade this worksheet?

This worksheet is available as a printable PDF and as a digital quiz on Wayground, and it includes a complete answer key. Assign the digital version for online responses, or print the PDF for written practice and grade submissions using the key. Printable student work can also be scanned with the Wayground for Teachers app.

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

Use the worksheet’s Advanced Settings to adjust font spacing or increase the font size so the equations, fractions, and multiple-choice options are easier to read. You can also apply a dyslexia-friendly font or translate the worksheet into another language when appropriate. These options preserve the worksheet’s focus on identifying slope, y-intercept, and equations from two points.

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 help students master essential skills and concepts. Browse more resources at https://wayground.com/en-us/worksheets.

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