Question

A line passes through the points R(-1,2) and S(1,-6). write the equation of the line through point A(2,0)that is parallel to line RS
A.y=4x-8
B.y=-4x+2
C.y=-4x+8
D.y=4x+2

Answer 1

$\text{The formula of a slope:}\\\\m=\dfrac{y_2-y_1}{x_2-x_1}\\\\\text{We have the points R(-1, 2) and S(1, -6)}\\\\\text{substitute:}\\\\m=\dfrac{-6-2}{1-(-1)}=\dfrac{-8}{2}=-4\\\\\text{therefore we have line RS in slope-intercept form:}\ y=-4x+b.\\\\\text{Parallel lines have the same slope.}\\\\\text{Therefore the line equation from question is y = -4x + b.}\\\\\text{It passes through the point A(2, 0).}\\\\\text{Substitute the coordinates of the point A to the equation of the line}:$

$0=-4(2)+b\\\\0=-8+b\qquad|+8\\\\8=b\to b=8$

$Answer:\ \boxed{C.\ y=-4x+8}$