Question

Find the equation of a line parallel to −4x−5y=−4 that contains the point (3,−2). Write the equation in slope-intercept form.

Answer 1

Answer:

see explanation

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 )

Rearrange - 4x - 5y = - 4 into this form

Add 4x to both sides

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

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

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

Parallel lines have equal slopes, thus

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

To find c substitute (3, - 2) into the partial equation

- 2 = - $\frac{12}{5}$ + c ⇒ c = - 2 + $\frac{12}{5}$ = $\frac{2}{5}$

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