# How do you find equation in slope intercept form of the straight line that has an x intercept of 5 & a y intercept of 10?

Feb 7, 2017

See the entire solution process below:

#### Explanation:

From the problem, because we were given the x and y-intercepts, we know two points on the line:

x-intercept = (5, 0) and y-intercept = (0, 10)

Knowing these points we can determine the slope. 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 gives:

$m = \frac{\textcolor{red}{10} - \textcolor{b l u e}{0}}{\textcolor{red}{0} - \textcolor{b l u e}{5}} = \frac{10}{-} 5 = - 2$

We can now use the slope intercept formula to find the equation of the line. 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.

Substituting again gives:

$y = \textcolor{red}{- 2} x + \textcolor{b l u e}{10}$