Slope-Intercept Form

CALCULATOR

—

Slope-Intercept Form Calculator

Find the slope-intercept form of a line using

Point 1:

(

DecFrac

,

DecFrac

)

Point 2:

(

DecFrac

,

DecFrac

)

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INTRO

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The general formula for slope-intercept form is

y

=

m

x

+

b

, where

m

represents the slope of the line, and

b

represents the

y

-value of the line’s

y

-intercept.

The slope-intercept form of a linear equation makes it easier for us to identify how steep a line is and where it crosses the $y$ -axis.

y

x

y = x

✨ Drag the points on the graph to see how they affect the equation of the line! ✨

When we're given , we first need to find the slope. Then, we can use the slope and one of the given points to solve for the $y$ -value of the $y$ -intercept and write the equation in slope-intercept form.

Given	Solve for Slope ( $m$ )	Solve for $y$ -value of $y$ -intercept ( $b$ )	Slope Intercept Form
Point 1: $(\underline{1}, \underline{1})$ Point 2: $(\underline{3}, \underline{5})$	$m = \frac{y _{2} - y _{1}}{x _{2} - x _{1}} = \frac{5 - 1}{3 - 1} = \frac{4}{2} = 2$	$\underline{y} \underline{1} 1 - 1 = m \underline{x} + b = 2 (\underline{1}) + b = 2 + b = b$	$y$ $=$ $m$ $x$ $+$ $b$ $y$ $=$ $2$ $x$ $+$ $($ $- 1$ $)$ $y = 2 x - 1$

What is Standard Form?

The general formula for the standard form of a linear equation is $A x + B y = C$ , where $A$ , $B$ , and $C$ are all integers.

We can go from standard form to slope-intercept form by isolating $y$ and simplifying:

2 x + 3 y = 12

⟹

3 y = - 2 x + 12

⟹

y = \frac{- 2 x + 1 2}{3}

⟹

y = - \frac{2}{3} x + 4

What is Point-Slope Form?

The general formula for the point-slope form of a linear equation is $y - y_{1} = m (x - x_{1})$ , where $m$ represents the slope of a line that contains the point ( $x_{1}$ , $y_{1}$ ).

We can go from point-slope form to slope-intercept form by isolating $y$ and simplifying:

y

-

2

=

- \frac{2}{3}

(x -

3

)

⟹

y = - \frac{2}{3} (x - 3) + 2

⟹

y = - \frac{2}{3} x + 2 + 2

⟹

y

=

- \frac{2}{3}

x

+

4

Check out our

Calculator

or explore our

Lesson

and

Practice

sections to learn more about slope-intercept form and test your understanding.

You can also use the Quick Links menu on the left to jump to a section of your choice.

You can also use the Quick Links dropdown above to jump to a section of your choice.

KEY STEPS

—

How to Find the Slope-Intercept Form of a Line

Find the slope-intercept form of a line using

Step 1. Solve for the slope ( $m$ ).

Remember, the slope is equal to the change in

y

divided by the change in

x

(rise over run).

Step 2. Solve for the $y$ -value of the $y$ -intercept ( $b$ ).

Plug the slope and the

x

and

y

of one of the given points into

y

=

m

x

+

b

, then solve for

b

Step 3. Replace $m$ and $b$ with their values in the $y = m x + b$ formula.

LESSON

— Using Two Points to Find the Slope-Intercept Form of a Line

PRACTICE

— Using Two Points to Find the Slope-Intercept Form of a Line

LESSON

— Using the Slope and One Point to Find the Slope-Intercept Form of a Line

PRACTICE

— Using the Slope and One Point to Find the Slope-Intercept Form of a Line

CONCLUSION

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Slope-Intercept Form