Question

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? Enter your answer in the box

Answer 1

3x+4y=16

Clarifying because other explanation was confusing

Just took review

Explanation:

Answer 2

Step 1

Find the slope of the given line

we have

`3x+4y=15`

Isolate the variable y

Subtract
`3x` both sides

`3x+4y-3x=15-3x`

`4y=-3x+15`

Divide by
`4` both sides

`y=-(3)/(4)x+ (15)/(4)`

the slope of the given line is

`m=-(3)/(4)`

Step 2

Find the equation of the line that passes through the point
`(8,-2)` 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 to

`y-y1=m(x-x1)`

we have

`m=-(3)/(4)`

`(x1,y1)=(8,-2)`

substitute in the equation

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

`y=-(3)/(4)x+6-2`

`y=-(3)/(4)x+4` or
`3x+4y=16`

therefore

the answer is

`y=-(3)/(4)x+4`

or

`3x+4y=16`