Question

Consider the line y = 5x - 3 Find the equation of the line that is parallel to this line and passes through the point (- 8, 2) Find the equation of the line that is perpendicular to this line and passes through the point (- 8, 2) Note that the ALEKS graphing calculator may be helpful in checking your answer

Answer 1

First, we know the slopes of perpendicular lines are negative reciprocals of each other. So, the negative reciprocal of -1 is 1. This is the slope of our new line. From here, we can use this new slope along with our given point to find the y-intercept (b) of our new equation:

y = mx + b

-4 = 1(-2) + b

-4 = -2 + b

-2 = b

The y-intercept of our new line is (0,-2). Now, we can write our equation of the new line:

y = x - 2