Question

What is an equation of the line that passes through the point (-4,3) and is

Answer 1

Answer:

5x + 4y = - 8

Step-by-step explanation:

The equation of a line in slope- intercept form is

y = mx + c ( m is the slope and c the y- intercept )

Given

4x - 5y = 20 ( subtract 4x from both sides )

- 5y = - 4x + 20 ( divide all terms by - 5 )

y = $\frac{4}{5}$ x - 4 ← in slope- intercept form

with slope m = $\frac{4}{5}$

Given a line with slope m then the slope of a line perpendicular to it is

$m_{perpendicular}$ = - $\frac{1}{m}$ = - $\frac{1}{\frac{4}{5} }$ = - $\frac{5}{4}$ , thus

y = - $\frac{5}{4}$ x + c ← is the partial equation

To find c substitute (- 4, 3) into the partial equation

3 = 5 + c ⇒ c = 3 - 5 = - 2

y = - $\frac{5}{4}$ x - 2 ← in slope- intercept form

Multiply through by 4

4y = - 5x - 8 ( add 5x to both sides )

5x + 4y = - 8 ← equation in standard form