Question

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

Answer 1

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 = 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`?