Question

What is an equation in slope-intercept form of the line that passes through (6, 10) and is parallel to the graph of y=1/3x−1?

Answer 1

Given:

The equation of line is

`y=(1)/(3)x-1`

To find:

The equation of line in slope-intercept form parallel to given line and passes through (6,10).

Solution:

The slope intercept form of a line is

`y=mx+b` ...(i)

where, m is slope and b is y-intercept.

The equation of given line is

`y=(1)/(3)x-1` ...(ii)

On comparing (i) and (ii), we get

`m=(1)/(3)`

Slope of given line is
`(1)/(3)`.

We know that slope of parallel lines are same. So, the slope of required line is
`(1)/(3)`.

Since slope of required line is
`(1)/(3)` and it passes through (6,10), therefore the equation of line is

`y-y_1=m(x-x_1)`

`y-10=(1)/(3)(x-6)`

`y-10=(1)/(3)(x)-(1)/(3)(6)`

`y-10=(1)/(3)(x)-2`

Add 10 on both sides.

`y-10+10=(1)/(3)(x)-2+10`

`y=(1)/(3)(x)+8`

Therefore, the required equation of line is
`y=(1)/(3)(x)+8`.