Question

What is the equation of a line parallel to the line y = 3x + 2, passing through the point (10,1)?

Answer 1

`y=3x-29`

Explanation:

First, let's find the slope of the line `y=3x+2`
As the equation is already in slope-intercept form `y=mx+c`,

Slope = `3`

Let a point `(x,y)` be on the new line.
By finding the slope again,

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

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

`y-1=3x-30`

Which can then be converted to different forms:

Standard form: `3x-y=29`
Equation form: `3x-y-29=0`
Slope-intercept form: `y=3x-29`

graph{3x-y=29 [-32.3, 47.7, -34.1, 5.9]}