# Converting to Slope Intercept Form Worksheet

### Before you start!

This 2-page worksheet gives more practice on equations in Slope Intercept Form (y = mx + b). These examples here show how the y-intercept is found, how to convert linear equations from standard to slope intercept form, and how to use this form to solve problems on slope and on the points on the line.

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## Equations in Slope Intercept Form (page 1 of 2)

Name:______________________

Convert the linear equations below given in standard form into Slope Intercept Form and write the slope and y-intercept for each. (the first one is done for you)

3x + 2y = 10

2y = -3x + 10
y = (-3x ÷ 2) + (10 ÷ 2)
y = -1.5x + 5
Slope is: -1.5
y-intercept is: 5

2x – 4y = 12

-4y = -2x + 12
y = (-2x ÷ (-4)) + (12 ÷ (-4))
y = 0.5x – 3
Slope is: 0.5
y-intercept is: -3

3x + 5y = 20

5y = -3x + 20
y = (-3x ÷ 5) + (20 ÷ 5)
y = -0.6x + 4
Slope is: -0.6
y-intercept is: 4

-x – 6y = 18

-6y = x + 18
y = (x ÷ (-6)) + (18 ÷ (-6))
y = -0.167x – 3
Slope is: -0.167
y-intercept is: -3

5x + 8y = 25

8y = -5x + 25
y = (-5x ÷ 8) + (25 ÷ 8)
y = -0.625x + 3.125
Slope is: -0.625
y-intercept is: 3.125

-3x + 12y = 24

12y = 3x + 24
y = (3x ÷ 12) + (24 ÷ 12)
y = 0.25x + 2
Slope is: 0.25
y-intercept is: 2

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## Equations in Slope Intercept Form (page 2 of 2)

Name:______________________

Find the equation of each of the lines (in slope intercept form) based on their slope and on a point through which each passes. (the first one is done for you)

Line passes through (3,1) with a slope of 2.

y = 2x + b
substituting x and y with 3 and 1 gives …
1 = (3 x 2) + b, ∴ b = 1 – 6, ∴ b = -5
equation of line is: y = 2x – 5

Line passes through (5,8) with a slope of 2.

y = 2x + b
substituting x and y with 3 and 1 gives …
8 = (2 x 5) + b, ∴ b = 8 – 10, ∴ b = -2
equation of line is: y = 2x – 2

Line passes through (-4,2) with a slope of 3.

y = 3x + b
substituting x and y with -4 and 2 gives …
2 = (3 x -4) + b, ∴ b = 2 – (-12), ∴ b = 14
equation of line is: y = 3x + 14

Line passes through (5,-2) with a slope of -0.5.

y = -0.5x + b
substituting x and y with 5 and -2 gives …
-2 = (-0.5 x 5) + b, ∴ b = -2 + 2.5, ∴ b = 0.5
equation of line is: y = -0.5x + 0.5

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## Related Resources

The various resources listed below are aligned to the same standard, (8EE06) taken from the CCSM (Common Core Standards For Mathematics) as the Expressions and equations Worksheet shown above.

Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b.

### Worksheet

Similar to the above listing, the resources below are aligned to related standards in the Common Core For Mathematics that together support the following learning outcome:

Understand the connections between proportional relationships, lines, and linear equations