# What are the intercepts for y = 6x + 8?

Oct 7, 2015

We find this out by setting either x or y to zero and solving the equation

#### Explanation:

The x-intercept is the point on a line where it crosses the x (horizontal) axis. That is, y = 0 at that point

graph{y=6x+8 [-15.48, 6.72, -0.9, 10.2]}

So, if we set y = 0, the equation becomes

$0 = 6 x + 8$

Solving for x by subtracting 8 from both sides of the equation:

$- 8 = 6 x$

and divide both sides by 6

$- \frac{8}{6} = x$

$x = - 1.333 \ldots \to$ this is the $x$-intercept

We can do the same thing for the y- intercept, which is the point where the line crosses the y (vertical axis), and x = 0

$y = 6 \left(0\right) + 8$

$y = 0 + 8$

$y = 8 \to .$ this is the $y$-intercept.

We can also take a shortcut... the equation of a line is:

$y = m \left(x\right) + b$

Where $m$ is the slope of the line, and $b$ is the $y$-intercept. So, in:

$y = 6 x + 8$

The $y$-intercept is $8$. Note that this only works when you have the equation in the form $y = m \left(x\right) + b$

Check the graph. Do these answers look about right? Does the line cross the x-axis at about $- 1.33$? Does it cross the y-axis at around $8$?