What are the lines on the graphs for the following?

Question

1. Graph a line that passes through (-3, 4) and is parallel to 2y = -x + 6.
2. Graph a line that passes through (2, -4) and is parallel to -3x + 2y = 8.

Answer 1

1. y=(-1/2)x + b, 4=(-1/2)(-3) + b, b=4-3/2 = 5/2, y=(-1/2)x + 5/2
2. y=(3/2)x + b, -4=(3/2)(2) + b, b= -4-3 = -7, y=(3/2)x -7

the parallel lines through the points are

y=(-1/2)x +5/2 and y= (3/2)x -7

parallel lines have the same slope. y=mx+b after plugging in the value of m, solve for b by plugging in the point. to find m, solve the equation for y. then the coefficient of the x term is the slope = m