MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

Answer:y = -3/4x + 4 or 3x + 4y = 16Step-by-step explanation:Step 1
Find the slope of the given linewe have3x + 4y = 15Isolate the variable y
Subtract 3x from both sides3x + 4y -3x = 15-3xDivide by 4 both sidesy = -3/4x + 15/4the slope of the given line ism = -3/4Step 2
Find the equation of the line that passes through the point and is parallel to the given line
we know that
if two lines are parallel, then their slopes are equal
The equation of the line into point-slope form is equal toy - y₁ = m(x-x₁)we havem= -3/4(x1,y1) = (8,-2)substitute in the equationy + 2= -3/4(x-8)y = -3/4x + 6 - 2y = -3/4x + 4 or 3x + 4y = 16therefore
the answer isy = -3/4x + 4or3x + 4y = 16