# How do you graph y=3x-2 using slope intercept form?

Feb 17, 2018

See a solution process below:

#### Explanation:

First, this equation is in slope-intercept form. 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.

$y = \textcolor{red}{3} x - \textcolor{b l u e}{2}$

Or

$y = \textcolor{red}{3} x + \textcolor{b l u e}{- 2}$

Therefore, we know the slope is: $\textcolor{red}{m = 3}$

And the $y$-intercept is: $\textcolor{b l u e}{b = - 2}$ or $\left(0 , \textcolor{b l u e}{- 2}\right)$

We can start graphing this equation by plotting the $y$-intercept:

graph{(x^2 + (y+2)^2 - 0.025) = 0 [-10, 10, -5, 5]}

Slope is defined as $\text{rise"/"run}$, or the amount the $y$ value changes compared to the $x$ value.

The slope for this equation is $m = 3$ or $m = 1$.

Therefore for each change in $y$ of $3$, $x$ changes by $1$.

We can now plot another point using this information: Now, we can draw a straight line through the two points to graph the equation:

graph{(y - 3x +2)(x^2 + (y+2)^2 - 0.025)((x - 1)^2 + (y - 1)^2 - 0.025) = 0 [-10, 10, -5, 5]}