What is an equation of the line that passes through the point (8,2) and is parallel to the line
5x−4y=36

5x - 4y = 32

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

5x - 4y = 36 ( subtract 5x from both sides )

- 4y = - 5x + 36 ( divide all terms by - 4 )

y = x - 9 ← in slope- intercept form

with slope m =

Parallel lines have equal slopes, thus

y = x + c ← is the partial equation

To find c substitute (8, 2) into the partial equation

2 = 10 + c ⇒ c = 2 - 10 = - 8

y = x - 8 ← in slope- intercept form

Multiply through by 4

4y = 5x - 32 ( subtract 4y from both sides )

0 = 5x - 4y - 32 ( add 32 to both sides )

32 = 5x - 4y, that is

5x - 4y = 32 ← in standard form

y=mx+b is the final answer!   : )