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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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Show AnswersName:______________________

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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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. *

- Equation of a Line - Determining & Plotting (4 Pages)
- Calculating the Slope of a Line (2 Pages)
- Slope Intercept Form (2 Pages)

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*

- Graphing Proportional Relationships (From Example/Guidance)
- Graphing Proportional Relationships (2 Pages) (From Worksheet)
- Calculating & Plotting Coordinates - from linear equations e.g. y = 2x - 6 ( 9 of 10) (From Worksheet)
- Calculating & Plotting Coordinates - from linear equations e.g. y = 2x - 6 ( 10 of 10) (From Worksheet)