Question

Solve for k such that a line passing through (-k, -5) and (-3, k+2) has a slope of 3/4. Show all work!

Answer 1

all work is shown and pictured and all complete

Answer 2

k = - 37

Explanation:

Calculate the slope m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₁ )

with (x₁, y₁ ) = (- k, - 5) and (x₂, y₂ ) = (- 3, k+2)

m =
`(k+2+5)/(-3+k)`, that is

`(k+7)/(-3+k)` =
`(3)/(4)` ( cross- multiply )

4(k + 7) = 3(- 3 + k) ← distribute both parenthesis

4k + 28 = - 9 + 3k ( subtract 3k from both sides )

k + 28 = - 9 ( subtract 28 from both sides )

k = - 37