# What is (4, 169) and (10, 385) in slope intercept form?

Jun 15, 2017

See a solution process below:

#### Explanation:

First, we need to determine the slope of the line running through the two points. The slope can be found by using the formula: $m = \frac{\textcolor{red}{{y}_{2}} - \textcolor{b l u e}{{y}_{1}}}{\textcolor{red}{{x}_{2}} - \textcolor{b l u e}{{x}_{1}}}$

Where $m$ is the slope and ($\textcolor{b l u e}{{x}_{1} , {y}_{1}}$) and ($\textcolor{red}{{x}_{2} , {y}_{2}}$) are the two points on the line.

Substituting the values from the points in the problem gives:

$m = \frac{\textcolor{red}{385} - \textcolor{b l u e}{169}}{\textcolor{red}{10} - \textcolor{b l u e}{4}} = \frac{216}{6} = 36$

The slope-intercept form of a linear equation is: $y = \textcolor{red}{m} x + \textcolor{b l u e}{b}$

Where $\textcolor{red}{m}$ is the slope and $\textcolor{b l u e}{b}$ is the y-intercept value.

We can substitute the slope we calculated for $m$ and the values from one of the points can be substituted for $x$ and $y$ and we can solve for $b$:

$385 = \left(\textcolor{red}{36} \cdot 10\right) + \textcolor{b l u e}{b}$

$385 = 360 + \textcolor{b l u e}{b}$

$- \textcolor{red}{360} + 385 = - \textcolor{red}{360} + 360 + \textcolor{b l u e}{b}$

$25 = 0 + \textcolor{b l u e}{b}$

$25 = \textcolor{b l u e}{b}$

$\textcolor{b l u e}{b} = 25$

We can now substitute the slope and value for $b$ we calculated into the formula to obtain the formula for the line:

$y = \textcolor{red}{36} x + \textcolor{b l u e}{25}$