# How do you find the slope and intercept to graph y = 5x - 9?

Nov 10, 2015

Looking at the $m$ and $c$ values of the equation.

#### Explanation:

General Form of a Straight Line Equation
The general form of an equation for a straight line is $y = m x + c$ In your case $m = 5$ and $c = - 9$

$m$ tells us the gradient or 'slope'. In your case this is 5, which means for every one coordinate you move along on the $x$ axis, your line will move up 5 coordinates in the $y$ axis.

The $y$ Intercept
As for the $y$ intercept, this is given by the value of $c$. In your case this is -9. Since we know that $x = 0$ on the $y$ axis then we know -9 is reffering to the $y$ coordinate. This means the $y$ intercept is at the coordinate $\left(0 , - 9\right)$

The $x$ Intercept
If you want to figure out the $x$ intercept as well then follow the method below.

On the $x$ axis we know that $y = 0$ we can put this into our equation and rearrange to find the value for $x$ at this point.

$0 = 5 x - 9$
$9 = 5 x$ (Add 9 to both sides)
$\frac{9}{5} = x$ (Divide by 5 on both sides)

We know know $x = \frac{9}{5}$ or $x = 1.8$

So the $x$ intercept is at the point $\left(1.8 , 0\right)$

This should be enough information to draw the graph!

Nov 10, 2015

See the explanation.

#### Explanation:

$y = 5 x - 9$ is in slope-intercept form for a linear equation, $y = m x + b$, where $m$ is the slope and $b$ is the y-intercept.

By definition, $5$ is the slope or $\left(\frac{5}{1}\right)$, and the y-intercept is $- 9$.

The y-intercept is the value of $y$ when $x = 0$.

$y = 5 \left(0\right) - 9 = - 9$
The point is $\left(0 , - 9\right)$

The x-intercept is the value of $x$ when $y = 0$.

$0 = 5 x - 9$

Add $9$ to both sides.

$9 = 5 x$

Divide both sides by $5$.

$\frac{9}{5} = x$

Switch sides.

$x = \frac{9}{5} = 1.8$
The point is $\left(\frac{9}{5} , 0\right)$

You can plot the x and y-intercepts and draw a straight line through the two points.

graph{y=5x-9 [-14.49, 17.53, -11.41, 4.61]}