The equation we are looking for must have the same slope as the given equation because we are told the two equations are parallel. By parallel it meant that the two equations do not meet or touch each other on the xy-plane.
Let's us change 5x + 2x = -8 to slope-intercept form as step 1. The slope-intercept form looks like this: y = mx + b, where m is the slope and b is the y-intercept.
5x + 2y = -8
2y = -5x - 8
Divide both sides by 2 to isolate y.
y = (-5/2)x - 4
The equation we are looking for has the slope (-5/2).
We now use the point-slope formula to find our equation.
Point-slope: y- y_1 = m(x - x_1), where m is the slope, y_1 is the y-coordinate of the given point and x_1 is the x-coordinate of the given point.
We now plug, chug and isolate y.
y - (-9) = (-5/2)(x - 8)
y + 9 = (-5/2)x + 20
y = (-5/2)x + 20 - 9
y = (-5/2)x + 11
Done!
