The line through (4,-1) and (k,5) is parallel to the line y=-3x+5. FInd the value of k.

k = 2

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

y = - 3x + 5 ← is in slope- intercept form

with slope m = - 3

Parallel lines have equal slopes, thus the 2 points have a slope of - 3

calculate the slope using the slope formula and equate to - 3

m =

with (x₁, y₁ ) = (4, - 1) and (x₂, y₂ ) = (k, 5)

m = = = - 3 ( multiply both sides by (k - 4) )

- 3(k - 4) = 6 ( divide both sides by - 3 )

k - 4 = - 2 ( add 4 to both sides )

k = 2