What is an equation of the line that passes through the point (8,-2) and is perpendicular to the line 4x - 3y =27

Answer 1

If you solve the given equation for y, you will have slope-intercept form.

4x - 3y = 27

4x - 27 = 3y

y = (4/3)x - 9

So, the slope of the given line is 4/3. Any line perpendicular to that line has a slope of -3/4 (negative reciprocal).

To write the equation of a line with a slope of -3/4 passing through (8, -2) you can either use point-slope or slope-intercept.

Using point-slope

y - (-2) = (-3/4)(x - 8)

y + 2 = (-3/4)x + 6

y = (-3/4)x + 4

Using slope-intercept

When x = 8, y = -2.

-2 = (-3/4)(8) + b

-2 = -6 + b

b = 4

So, y = (-3/4)x + 4

Here is a graph showing the above as well as how to find the point of intersection of the two lines.

desmos.com/calculator/2bam0gqmu5