A line is parallel to y=5x+9 and intersects the point (-2, -3). What is the equation of this parallel line?

Answer 1

Parallel lines share the same slope, by definition. Thus, the parallel line that you are looking for will be of the form y = 5x + b. Since you know that the line passes through the point (-2, 3), (-2, 3) is a solution to the equation of the line. By substitution,

-3 = 5(-2) + b

-3 = -10 + b

7 = b

Thus, the parallel line is given by y = 5x + 7.