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=(y_2-y_1)/(x_2-x_1)\\\\\text{We have the points R(-1, 2) and S(1, -6)}\\\\\text{substitute:}\\\\m=(-6-2)/(1-(-1))=(-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}`