Write an equation in slope-intercept form for the line that passes through the given point and is perpendicular to the given line.

Question

1. (5,-1); y=4x-7
2. (4,-2); y=3

Please explain what you did so I can learn, thanks!

Answer 1

1.   (5,-1); y=4x-7

The Slope of this given line is 4. The slope of the line perpendicular is always the opposite reciprocal. That means the Slope will be – ¼. Use point-slope from.  y – y1 = m(x – x1) with this Slope and the given point

y – (-1) = (-1/4)(x – 5) multiply both sides by - 4 -- on the right side, - 4(-1/4) =1

- 4(y + 1) = (x – 5) distribute

-4y – 4 = x – 5  add 4

-4y = x – 1  divide by – 4

y = (-1/4)x + (1/4). That is in slope-intercept from.

2.   ( 4,-2); y=3

This is the equation of a horizontal line (there is no x variable so you should know that is horizontal.

The line perpendicular to a horizontal line is a vertical line. The equation of a vertical line is x = a where a is the x-coordinate of every point on the line. That means the equation you are looking for is. x = 4

Patti D.