# How do you find the slope and intercept of 3x+7=0?

Jun 14, 2018

The slope is 3 and the intercept is 7.

#### Explanation:

First off the equation should read $3 x + 7 = y$ just easier to make sense of.

The values you are looking for are in the formula:

The slope is a ratio of how much $y$ increases based on how much $x$ increases, it's usually calculated based on the "rise over run" it looks like this:

$\text{rise (increase in y)"/"run (increase in x)}$

In the case of this formula, $y$ increases 3 units for every unit $x$ increase. I'll put a graph in and you can pick any 2 points on the line and find the amount $x$ and $y$ increases (say y=0;x=5 and y=15;x=10 then in amount y increases is 15 units while x increases by 5) then the slope is calculated like this:

$\frac{15}{5} = 3$ This gives you the 3 in the equation $\textcolor{red}{3} x + 7 = y$

The intercept is the value of $y$ when $x$ equals 0. If you substitute $x = 0$ into the equation you can see that the only thing left to that gives a value is 7.

$\cancel{3 \left(0\right)} + 7 = y \to y = 7$ When $x = 0$ So 7 is your intercept.

graph{3x+7 [-12.3, 16.17, -2.06, 12.18]}

Jun 14, 2018

$\text{see explanation}$

#### Explanation:

$\text{subtract 7 from both sides and divide by 3 gives}$

$x = - \frac{7}{3}$

$\text{this is the equation of a vertical line parallel to the y-axis}$
$\text{passing through all points with an x-coordinate of } - \frac{7}{3}$

$\text{the slope is therefore undefined}$

$\text{the x-intercept "=-7/3" there is no y-intercept}$
graph{(y-1000x-2333)=0 [-10, 10, -5, 5]}