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

Question

8500 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-10-07T14:39:12

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

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

$0 = 6x + 8$

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

$-8 = 6x$

and divide both sides by 6

$- 8/6 = x$

$x = -1.333... ->$ 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

$y = 6(0) + 8$

$y = 0 + 8$

$y = 8 ->.$ this is the $y$ -intercept.

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

$y = m(x) + b$

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

$y = 6x + 8$

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

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 $8$ ?

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