Question

What is an equation of the line that passes through the point (8,-8)(8,−8) and is perpendicular to the line 4x-3y=184x−3y=18?

Answer 1

Answer:

The equation of the line is $y = -\frac{3x}{4} - 2$

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

$y = mx + b$

In which m is the slope and b is the y-intercept.

Perpendicular lines:

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to the line 4x-3y=18

First, we place this line into the format, to find the slope:

$4x - 3y = 18$

$3y = 4x - 18$

$y = \frac{4x}{3} - 6$

This line has slope 4/3. So, for the perpendicular line, the slope will be of m as such:

$\frac{4m}{3} = -1$

$4m = -3$

$m = -\frac{3}{4}$

So the desired line will have an equation in the following format:

$y = -\frac{3x}{4} + b$

Passes through the point (8,-8)

We use this to find b. This point means that when $x = 8, y = -8$. So

$y = -\frac{3x}{4} + b$

$-8 = -\frac{3*8}{4} + b$

$-8 = -6 + b$

$b = -2$

So

$y = -\frac{3x}{4} - 2$