Question

What is the equation of the line that is parallel to 8x-5y=2 and goes through the point (-5,-2)

Answer 1

Answer:

8x - 5y = - 30

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 8x - 5y = 2 into this form

Subtract 8x from both sides

- 5y = - 8x + 2 ( divide all terms by - 5 )

y = $\frac{8}{5}$ x - $\frac{2}{5}$ ← in slope- intercept form

with slope m = $\frac{8}{5}$

• Parallel lines have equal slopes, hence

y = $\frac{8}{5}$ x + c ← is the partial equation of the parallel line

To find c substitute (- 5, - 2) into the partial equation

- 2 = - 8 + c ⇒ c = - 2 + 8 = 6

y = $\frac{8}{5}$ x + 6 ← in slope- intercept form

Multiply through by 5

5y = 8x + 30 ( subtract 5y from both sides )

0 = 8x - 5y + 30 ( subtract 30 from both sides )

8x - 5y = - 30 ← in standard form