Question

How do you write an equation for a line that is parallel to `y=3x+7` and passes through (2,10)?

Answer 1

`y=3x+4`

Explanation:

`y=mx+b`

Where `m` is the slope and `b` is the y intercept

The slope of the given equation, `y=3x+7` is `3`

So, to write an equation parallel to the given equation and set of points, use point slope form and the slope of `3`:

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

Where `(2,10)=>(x_1,y_1)` and `m=3`

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

Distribute the `3` throughout the set of parenthesis

`y-10=3x-6`

Perform the opposite operation to isolate `y` by adding `10` on both sides of the equation

`y=3x+4`

As you can see, the slope of this line is `3`, which means that the two equations are parallel to each other