Consider two parallel line segments.

Part A: Find the slope of segment CD with endpoints C(−7, −2) and D(−4, 2). Show your work. (2 points)

Part B: What is the value of y so that segment AB with endpoints A(4, y) and B(7, 4) is parallel to segment CD question mark Show your work. (2 points)

see explanation

Step-by-step explanation:

A

Calculate the slope m using the slope formula

m =

with (x₁, y₁ ) = C(- 7, - 2) and (x₂, y₂ ) = D(- 4, 2)

m = =

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B

Parallel lines have equal slopes.

Calculate the slope of AB and equate to the slope of CD

(x₁, y₁ ) = A(4, y) and (x₂, y₂ ) = B(7, 4)

m = , that is

    = = ( cross- multiply )

3(4 - y) = 12 ( divide both sides by 3 )

4 - y = 4 ( subtract 4 from both sides )

- y = 0 ⇒ y = 0

step-by-step explanation:

first, eliminate the parenthesis:

3

x

+

2

−

4

x

second, group like terms:

3

x

−

4

x

+

2

third, combine like terms:

(

3

−

4

)

x

+

2

→

−

1

x

+

2

→

−

x

+

2