Please help me with this geometry question.

Question

A line passes through the points R(-2,5) and S(-1,2). Write and equation of the line through a point A(5,0) that is parallel to RS.

A. y = -3x + 15

B. y = -3x - 5

C. y = 3x + 15

D. y = 3x - 5

Answer 1

Use the point-slope form of an equation to determine the slope of a line that goes through the two given points:

yS - yR = m(xS - xR)

2 - 5 = m(-1 + 2)

m = -3

Since we are looking for a line that is parallel to the line that we found, we want a line that has a slope of -3. This narrows our options to A. and B.

Now we use A(5, 0) and m = -3 to determine the equation of the new parallel line:

y - 0 = (-3)(x - 5)

y = -3x + 15

This is the answer in A.

Answer 2

Equation of line is y = mx + b, where m is slope and b is y-intercept

First find the slope of RS: (2-5)/(-1-(-2)) = -3/1 = -3

Slope of parallel line (m) is -3, so we have y = -3x + b

Plug in A(5,0) for x and y: 0 = -3(5) + b; b = 15

equation of line is y= -3x + 15 (A)