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Teachers & SchoolsStudy Guide

If the equation of a line is in **slope-intercept form**, it looks like this:

*y = mx + b*

Here's what those extra letters mean:

*m*is the**slope**of the line.*b*is the.*y*-intercept

Let's look at a few examples:

The equation *y* = 2*x* + 1 is in slope-intercept form. The coefficient of the *x*-term is 2, so the slope is 2. The constant is 1, so the *y*-intercept is 1. That means the graph passes through the point (0, 1).

In the equation *y* = 4 â€“ 8*x*, the slope is -8 (the coefficient of the *x*-term) and the *y*-intercept is 4. Don't let the order of the terms trip you up: we can rearrange it so it looks like *y* = -8*x* + 4.

In the equation *y* = -9*x*, the slope is -9 and the *y*-intercept is 0, since there's no constant.

Remember: the slope (*m*) is equal to the change in *y* divided by the change in *x*, or "rise over run."

Let's examine how to graph an equation in slope-intercept form. What does the graph of *y* = 2*x* + 1 look like?

Our equation is in slope-intercept form, so we know that the number in front of *x* is the slope (2), and 1 is the *y*-intercept.

We start by plotting the *y*-intercept.

Next, since we know that the slope is 2, also known as , we know that another point will be 2 units up and 1 unit over (in the positive direction of course).

Finally, we connect these points.

What if the equation isn't solved for *y* already? Well, we'll just have to solve it for *y*, won't we ?

Graph 2*x* + 3*y* = 18.

First things first: solve for *y* by subtracting the 2*x* term and dividing by 3.

Now our equation is in slope-intercept form and we can graph it.

We put a point at 6 on the *y*-axis since 6 is the *y*-intercept. From there, we "rise" -2, which means we go *down* 2 units, but we don't put a point there yet. We still need to "run" 3 to the right. Then we put the point down.

*Look Out:** when using slope-intercept form to graph lines, always make sure the equation is solved for y so that the equation is in the form y = mx + b*.