Question

What is the equation of the line that has a slope of 4 and goes through `(1,9)`?

Answer 1

`y=4x+13`

Explanation:

When you are given the slope and a set of points, you use point slope form, which is:

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

Where `m` is the slope, `y_1` is the `y` in the set of points, and `x_1` is the `x` in the set of points

So, plug in your numbers

`y-9=4(x-1)`

Distribute the `4` throughout the set of parenthesis on the right

`y-9=4x-4`

Begin to isolate y by adding `9` on both sides of the equation

`y=4x+5`

Answer 2

The equation in point-slope form is `y - 9 = 4(x - 1)`.

Explanation:

Use the point-slope form of a linear equation, which is
`y - y_1 = m(x - x_1)`
where m is the slope of the line and `(x_1, y_1)` is a point on the line.

`y - 9 = 4(x - 1)`

If the answer needs to be in slope-intercept form, solve the equation for `y`:

`y - 9 = 4(x - 1)`
`y - 9 = 4x - 4`
`y - 9 + 9 = 4x - 4 + 9`
`y = 4x + 5`

If the answer needs to be in standard form, continue using inverse operations to take the equation from slope-intercept form to standard form.

`y = 4x + 5`
`-4x + y = 4x - 4x + 5`
`-4x + y = 5`
`-1(-4x + y = 5)`
`4x - y = -5`