# What is the slope-intercept form of the equation with a slope of 4/3 and which goes through the point (-2, -0)?

Aug 18, 2017

See a solution process below:

#### Explanation:

We can use the point-slope formula to find the equation for this slope and point. 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.

First we can substitute the slope for $\textcolor{red}{m}$ giving:

$y = \textcolor{red}{\frac{4}{3}} x + \textcolor{b l u e}{b}$

Next, we can substitute the values from the point in the problem and solve for $\textcolor{b l u e}{b}$:

$0 = \left(\textcolor{red}{\frac{4}{3}} \times - 2\right) + \textcolor{b l u e}{b}$

$0 = - \frac{8}{3} + \textcolor{b l u e}{b}$

$\textcolor{red}{\frac{8}{3}} + 0 = \textcolor{red}{\frac{8}{3}} - \frac{8}{3} + \textcolor{b l u e}{b}$

$\frac{8}{3} = 0 + \textcolor{b l u e}{b}$

$\frac{8}{3} = \textcolor{b l u e}{b}$

We can substitute $\frac{8}{3}$ for $\textcolor{b l u e}{b}$ and the slope from the problem to write the equation:

$y = \textcolor{red}{\frac{4}{3}} x + \textcolor{b l u e}{\frac{8}{3}}$