Writing equations of lines parallel and perpendicular to a given line through a point

Question

Consider the line



Find the equation of the line that is parallel to this line and passes through the point (−7,  5)

Find the equation of the line that is perpendicular to this line and passes through the point (−7,  -5)

Answer 1

1) A parallel line should have the same slope: m = -6/7. To find the equation of the line, we will use m = -6/7, x = -7, and y = 5, then solve for the y-intercept b.

y = mx + b

5 = (-6/7)(-7) + b

5 = 6 + b

-1 = b

So our equation is y = -6/7x - 1

2) We will carry out the exact same process except that our slope will be the opposite reciprocal of our original slope: m = 7/6. Also note that this time x = -7 and y = -5

y = mx + b

-5 = (7/6)(-7) + b

-5 = -49/6 + b

19/6 = b

So our equation is y = 7/6x + 19/6

Please let me know if you have any questions!