# How do you find the slope and intercept to graph 2x+y=7?

Nov 6, 2015

Manipulate the equation into the slope-intercept form $y = m x + b$ to find the slope $m = - 2$ and y-intercept $b = 7$

#### Explanation:

The simplest method of finding the slope and y-intercept of a linear equation is to put it into the slope-intercept form of $y = m x + b$ where $m$ is the slope and $b$ is the y-intercept.

Starting from $2 x + y = 7$, all we need to do is subtract $2 x$ from each side of the equation to obtain $y = - 2 x + 7$

The equation is then in slope-intercept form, where $m = - 2$ and $b = 7$

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Let's take a look at why the y-intercept and slope are represented by $b$ and $m$.

First, note that the y-intercept is the point on the graph where $x = 0$
So, setting $x = 0$ in the equation $y = m x + b$ gives $y = b$, showing that the graph intersects the y-axis at $\left(0 , b\right)$.

Next, note that as $b$ remains constant, if you increase the value of $x$ by $1$ from any initial value, the value of $y$ increases by $m$. So, by the $\text{slope"="rise"/"run}$ formula, we have a rise of $m$ for a run of $1$, meaning the slope of the graph is $\frac{m}{1} = m$.