Definition of Slope Intercept Form

Slope intercept form is one of the most common ways to represent the equation of a line. It represents the slope and y-intercept point. The formula for slope intercept formula is given as:

y = mx + b

Where m is the slope of the line, and b is the y-coordinate where the line intersects the y-axis, known as the y-intercept.

Slope intercept form allows us to quickly draw a line in the x-y coordinate system. In this lesson, we will go through how to get a line's equation into slope intercept form.

How to Find the Slope Intercept Form of a Line

Often, we need to find the slope intercept equation of a line from discrete points on its graph. There are two easy steps to follow for getting the slope intercept form. Remember that we need the slope of the line and the y value where the line crosses the y-axis.

1.) To find the slope of the line m, use the general slope formula m = ^rise/_run. In the x-y coordinate system, we will apply the slope formula as:

m = ^{y₂ - y₁}/_{x2 - x1}

2.) Once the slope m is determined, we can find the y-intercept. There are two ways to do this. If possible, we should look at the line and visually determine where it crosses the y-axis. If the exact y-intercept is not visually clear than we can use one of our known points and our known slope to find it. The equation for using a point and the slope to find our y-intercept b is given as:

b = y₁ - mx₁

Where x₁ and y₁ are the coordinates of a known point on the line. Once we solve for b, we may plug that and our m value into the slope intercept equation.

How to Convert Standard Form to Slope Intercept Form Example Problem

The standard form equation of a line is Ax + By = C. We can use simple algebraic operations to rearrange this form into y = mx + b slope intercept form.

Let's go through an example to see how a standard form equation can be rearranged to slope intercept form.

Let's use the standard form line equation 5x + 2y = 8. Our goal is to isolate y while making algebraically sound operations.

1. First, let's subtract the term 5x from both sides.
2. Now we have 2y = -5x + 8. Next, divide both sides by 2 to finish isolating y.
3. y = -2.5x + 4 is the equation of our line in slope intercept form.