Question

What is the equation of the line with slope `m= -3` that passes through `(23,23)`?

Answer 1

Substitute the variables in the equation for our numbers.

Explanation:

This is the slope-intercept equation:

`y=mx+b`

The letter `m` is the slope (-3) and the letters `y` and `x` are our x- and y-variables (both of which are 23).

Our equation is this:

`23=-3(23)+b`

From here, we solve for `b`:

`-3⋅23=-69`

`23=-69+b`

`92=b`

We now know that b=92, so we can plug it back into our equation to get our answer. Since this is an equation with an infinite number of coordinates on it, the only numbers we're going to put in are the slope and b. This is what we get:

y=-3x+92