Question

What is the equation of the line passing through `(2,17)` and `(1,-2)`?

Answer 1

`y=19x-21`

Explanation:

First off, I am assuming that this equation is linear. Once I do that, I know that I can use the formula `y=mx+b`. The `m` is the slope and the `b` is the x-intercept. We can find the slope by using the `(y2-y1)/(x2-x1)`

Let's start by plugging in the information we have, like this:
`(-2-17)/(1-2)`, which simplifies to `(-19)/-1` or just `19`. That means the slope is `19`, and all we need is what `y` equals when `x` is `0`. We can do this by looking at the pattern.
`x` `color(white)(..........)` `y`
2`color(white)(..........)` 17
`color(white)(................)`)+19
1 `color(white)(.......)` `-2`
`color(white)(................)`)+19
`color(red)(0)` `color(white)(.......)` `color(red)(-21)`

So, with this table I can tell that the `x`-intercept (when `x=0`, `y=?`) is `(0, -21)`. Now we know our `b` part of the equation.

Let's put it together:
`y=mx+b`
`y=19x-21`

Let's graph the equation we have and make sure it passes through the right points, `(2,17)` and `(1,-2)`
graph{y=19x+(-21)}

The graph fits those points so the equation is correct!