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

Jan 31, 2016

$y = 19 x - 21$

#### Explanation:

First off, I am assuming that this equation is linear. Once I do that, I know that I can use the formula $y = m x + b$. The $m$ is the slope and the $b$ is the x-intercept. We can find the slope by using the $\frac{y 2 - y 1}{x 2 - x 1}$

Let's start by plugging in the information we have, like this:
$\frac{- 2 - 17}{1 - 2}$, which simplifies to $\frac{- 19}{-} 1$ 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$$\textcolor{w h i t e}{\ldots \ldots \ldots .}$ $y$
2$\textcolor{w h i t e}{\ldots \ldots \ldots .}$ 17
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .}$)+19
1 $\textcolor{w h i t e}{\ldots \ldots .}$ $- 2$
$\textcolor{w h i t e}{\ldots \ldots \ldots \ldots \ldots .}$)+19
$\textcolor{red}{0}$$\textcolor{w h i t e}{\ldots \ldots .}$$\textcolor{red}{- 21}$

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

Let's put it together:
$y = m x + b$
$y = 19 x - 21$

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

The graph fits those points so the equation is correct!