Question

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

Answer 1

Answer:

x - 3y = -12

Step-by-step 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    

Step-by-step 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

                                   $y=\frac{1}{3}x+2$

Slope of line is $m=\frac{1}{3}$

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

Here (x₁,y₁) =  (3, 5)

Substituting

             $y-5=\frac{1}{3}(x-3)\\\\3y-15=x-3\\\\3y-x=12$

Equation of line is 3y-x=12