Question

What is the equation of a line that is parallel to −x+3y=6 and passes through the point (3, 5) ?

Enter your answer in the box.

Answer 1

x - 3y = -12

Explanation:

First find the slope by converting the given equation to slope-intercept form.

-x + 3y = 6

3y = x + 6

y = 1/3x + 2

- meaning that the slope = 1/3.

Y - y1 = m(x - x1) where m = 1/3 and (x1, y1) = (3, 5):-

y - 5 = 1/3(x - 3) Multiply each tern by 3:-

3y - 15 = x - 3

x - 3y = -12 is the required equation

Answer 2

Equation of line is 3y - x =12

Explanation:

Parallel lines has same slope

Here line is parallel to −x+3y=6

Changing it to y = mx + c form

−x+3y=6

3y = x + 6

`y=(1)/(3)x+2`

Slope of line is
`m=(1)/(3)`

We have equation line with slope m and passing through (x₁,y₁) as (y-y₁)=m(x-x₁)

Here (x₁,y₁) = (3, 5)

Substituting

`y-5=(1)/(3)(x-3)\\\\3y-15=x-3\\\\3y-x=12`

Equation of line is 3y-x=12