Find the equation of a line that passes through (5,-3) and is perpendicular to y = x.

Answer 1

Hi Malaak K

y = -x + 2

y = x

In Slope intercept form is

y = mx + b

where m is 1 and b is 0

Perpendicular lines have inverse slopes with opposite signs

For the perpendicular line the slope is -1

y = mx + b for your perpendicular line starts below

y = -1x + b

Use the coordinates given (5, -3) to solve for b

-3 =-5 + b

-3 + 5 = b

2 = b

y = -x + 2

You can graph both lines on the same grid at Desmos.com to see that they are perpendicular and the line

y = -x + 2 passes through (5, -3). I hope this helps

Answer 2

The slope of y = x has slope of 1.

The line that is perpendicular to y=x should have slope of -1 (negative reciprocal of 1)

Now the question becomes point-slope formula y - given y = slope (x - given x)

y-(-3) = -1 (x-5)

y+3 = -x +5

y = -x + 2. Done!