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

the simplified form is

step-by-step explanation:

we want to simplify the expression,

let us change the middle bar to a normal division sign to obtain,

we multiply the first fraction by the reciprocal of the second fraction to obtain,

we factor to obtain,

we cancel the common factors to get,

we simplify to get,

the correct answer is b