Plz , 15 points!

what is the equation of a line that passes through the point (8, −2) and is parallel to the line whose equation is 3x + 4y = 15?

3x + 4y = 16.

Step-by-step explanation:

First work out the slope of the given equation:

3x + 4y = 15

4y = -3x + 15

y = -3/4x + 15/4.

The required line has the same slope,  = -3/4.

Using the point-slope equation:

y - y1 = m(x - x1)

y - (-2) = -3/4(x - 8)

y + 2 = -3/4x + 6

y = -3/4x + 4

Convert to standard form:

Multiply by 4:

4y = -3x + 16

3x + 4y = 16.

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17