*What is slope-intercept form?* This article is here to help!

Read below to learn how to write equations in slope-intercept form. We’ll also discover how to find slope-intercept form from two points, from a slope and a point, and from a graph. Additionally, we will see how to determine the x-intercepts and y-intercepts.

Changing an equation into a certain form can help us to identify useful information. Just like we can change play-dough or clay from one shape to another, we can change equations to reveal the information we need. Let’s learn more about slope-intercept form!

What We Review

## What is slope-intercept form?

The slope-intercept form of an equation is:

### What is the b?

The variable b represents the **y-intercept**. This is where the line crosses the y-axis.

### What is the m?

The variable m represents the **slope**.

Remember, slope of a linear equation is often described as \frac{\text{rise}}{\text{run}}. For more info on slope, visit our review article on how to find slope.

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## Slope-intercept equation from two points (example)

To determine how to write an equation from two points, we must determine the value of the slope and the y-intercept. First, we will calculate the slope. This will be the value of m in the slope-intercept form equation:

y=mx+b

Let’s answer the question, “What is the slope-intercept form of a line going through the points (1,5) and (-4,7)?”

Remember, to calculate the slope we use the equation:

\dfrac{y_2-y_1}{x_2-x_1}

First, we can label the points.

Now, we can substitute the values into the slope equation.

\dfrac{y_2-y_1}{x_2-x_1}

\dfrac{7-5}{-4-1}

\dfrac{2}{-5}

\dfrac{-2}{5}

Therefore, the slope of the line is \frac{-2}{5}. We can substitute \frac{-2}{5} for m.

y=mx+b

y=\dfrac{-2}{5}x+b

Now, we must determine the value of b. To do so, we will use one point and substitute the values of x and y. Let us use the point (1,5). We will substitute 1 for x and 5 for y.

y=\dfrac{-2}{5}x+b

5=\dfrac{-2}{5}1+b

5=\dfrac{-2}{5}+b

5+\dfrac{2}{5}=b

\dfrac{25}{5}+\dfrac{2}{5}=b

\dfrac{27}{5}=b

Therefore, the value of b is \frac{27}{5}, which is the y-intercept. We will now substitute \frac{27}{5} for b.

y=\dfrac{-2}{5}x+b

**y=\dfrac{-2}{5}x+\dfrac{27}{5}**

For an additional example of writing an equation from two points, watch the video below:

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## Slope-intercept equation given slope and y-intercept (example)

Instead of being given two points, we may need to know how to find slope-intercept form with slope and the y-intercept. In this example, we will use a slope of -4 and a y-intercept of \frac{1}{5}.

Remember, the slope is represented by m and the y-intercept is represented by b. We will simply substitute the given values for m and b. We start with form:

y=mx+b

**y=-4x+\dfrac{1}{5}**

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## Find slope-intercept equation from graph (example)

Similarly, when we need to know how to write slope-intercept form from a graph, we determine the slope and the y-intercept.

When presented with a graph, we must first determine two points on the grid lines and identify those points.

For our graph, we will use the points (1,1) and (0,-2). Now, we determine the rise and the run. Slope is \frac{\text{rise}}{\text{run}}. For us, the rise is how far up we must travel to get from (0,-2) to get to (1,1). The run is how far to the right we must travel to get from (0,-2) to get to (1,1). Let us determine these values by counting on the graph.

- The
**rise**, the vertical change shown in blue, is 3. - The
**run**, the horizontal change shown in green, is 1. - Therefore, the
**slope**is \frac{\text{rise}}{\text{run}} or \frac{3}{1}

This means, the slope of the line is 3.

The y-intercept is where the line crosses the y-axis, the vertical axis. In this case, the line crosses the y-axis at the point (0,-2), so the y-intercept is -2.

Because the slope is 3 and the y-intercept is -2, we will substitute 3 for m and -2 for b to create the slope-intercept form of the equation.

y=mx+b

y=3x+(-2)

**y=3x-2**

If you’re a visual learner, below is a brief video example of writing a slope-intercept equation from a graph:

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## Calculate x and y intercepts from slope-intercept form (example)

Consider the slope-intercept form equation y=6x+9. We can determine the x and y-intercepts. The x-intercept occurs when y equals 0, and the y-intercept occurs when x equals 0. We can determine the x-intercept by setting the value of y equal to 0.

y=6x+9

0=6x+9

-9=6x

\dfrac{-9}{6}=x

\dfrac{-3}{2}=x

Therefore, the x-intercept of the equation is \frac{-3}{2}. This means the graph will cross the x-axis when x equals \frac{-3}{2}.

Because the equation is written in slope-intercept form, we can easily determine the y-intercept. The y-intercept is the value of b in the equation.

y=mx+b

y=6x+9

Because we can see that 9 is the value of b, we know that the y-intercept of the equation is 9.

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## Other forms of linear equations

Linear equations can also be written in **point-slope form**, determined by one point on the line and the slope of the line. To learn more, read our detailed review article on point-slope form.

A linear equation can also be written in **standard form**. This form can be very useful to solve systems of equations. To learn more, read our review guide on the standard form of linear equations.

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## Summary: Slope-Intercept Form

- Remember, slope-intercept form is:
**y=mx+b**. - We have determined slope-intercept form using a graph, using a point and a slope, and using two points.
- We have also found x and y-intercepts from an equation in slope-intercept form.

Looking for video summary of this content? Checkout this helpful 5-minute video explanation of slope-intercept form.

*Click here to explore more helpful Albert Algebra 1 review guides.*

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