Parallel lines have equal slope but different y-intercepts.
slope intercept form:
y = mx + b (where m = slope
and b = y-intercept)
simply subtract 9 from both sides of the given equation to get slope intercept form of the first line:
y + 9 = -3/2x
y + 9 - 9 = -3/2x - 9
y = -3/2x - 9
so the slope (m) = -3/2
the problem tells us a point on the second line (x,y) or (-8,9)
and we now know slope is -3/2
so let’s plug those in and solve for the y-intercept (b) of the second line.
y = mx + b
9 = -3/2(-8) + b
9 = 12 + b
9 - 12 = 12 - 12 + b
-3 = b
so now we know the slope (m) of both lines is -3/2 and the y-intercept (b) of the second line is -3
all we have to do is use the information to establish slope intercept form of the equation of the second line:
y = mx + b
y = -3/2x - 3
The answer is: y = -3/2x - 3
check your answer by plugging the point (-8,9) back in to your equation
9 = -3/2(-8) - 3
9 = 12 - 3
9 = 9 [TRUE]