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

Explanation:

Use the point-slope formula by the line

y - y_1 = m(x - x_1) when x_1 =8 and y_1 = -2 m : is the slope (same slope for the line whose equation is 3x + 4y = 15 because are parallel)

calculate : m

3x + 4y = 15

4y = -3x +15

y = (-3/4)x +15/4 so m = -3/4

an equation is : y +2 =(-3/4)(x-8)

Answer 2

The required equation of line is
`3x+4y=16`

Explanation:

Given : A line that passes through the point (8, -2) and is parallel to the line whose equation is
`3x + 4y = 15`

To find : What is the equation of a line ?

Solution :

We know that,

When two lines are parallel then their slopes are equal.

The equation of line is
`3x + 4y = 15`

Convert into slope form
`y=mx+c`,

`4y =-3x+ 15`

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

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

The slope of the line is
`m=-(3)/(4)`

The line passes through (8,-2).

The general point slope form is
`(y-y_1)=m(x-x_1)`

i.e.
`(y-(-2))=-(3)/(4)(x-8)`

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

`4y+8=-3x+24`

`3x+4y=16`

Therefore, the required equation of line is
`3x+4y=16`