Convert equation to slope intercept form calculator

The slope-intercept form calculator will find the slope of the line passing through the two given points, its y-intercept, and the slope-intercept form of the line, with steps shown.

Related calculators: Line Calculator, Slope Calculator, Parallel and Perpendicular Line Calculator

Your Input

Find the equation of a line given two points $$$P = \left(-1, 5\right)$$$ and $$$Q = \left(3, 7\right)$$$.

Solution

The slope of a line passing through two points $$$P = \left(x_{1}, y_{1}\right)$$$ and $$$Q = \left(x_{2}, y_{2}\right)$$$ is given by $$$m = \frac{y_{2} - y_{1}}{x_{2} - x_{1}}$$$.

We have that $$$x_{1} = -1$$$, $$$y_{1} = 5$$$, $$$x_{2} = 3$$$, and $$$y_{2} = 7$$$.

Plug the given values into the formula for a slope: $$$m = \frac{7 - 5}{3 - \left(-1\right)} = \frac{1}{2}$$$.

Now, the y-intercept is $$$b = y_{1} - m x_{1}$$$ (or $$$b = y_{2} - m x_{2}$$$, the result is the same).

$$$b = 5 - \left(\frac{1}{2}\right)\cdot \left(-1\right) = \frac{11}{2}$$$

Finally, the equation of the line can be written in the form $$$y = b + m x$$$:

$$$y = \frac{x}{2} + \frac{11}{2}$$$

Answer

The slope of the line is $$$m = \frac{1}{2} = 0.5$$$A.

The y-intercept is $$$\left(0, \frac{11}{2}\right) = \left(0, 5.5\right)$$$A.

The equation of the line in the slope-intercept form is $$$y = \frac{x}{2} + \frac{11}{2} = 0.5 x + 5.5$$$A.

About Slope Intercept Form (y=mx+b) Calculator

The Slope Intercept Form Calculator is used to help you find the slope intercept form for the equation of the straight line (y=mx+b) that passes through two points. It also calculates the slope and the y-intercept of the line.

FAQ

The slope m of the line through any two points (x1, y1) and (x2, y2) is given by:

The y-intercept b of the line is the value of y at the point where the line crosses the y axis. Since for point (x1, y1) we have y1 = mx1 + b, the y-intercept b can be calculated by:

b = y1 - mx1

To calculate Slope Intercept Form you need input two points (x1, y1) and (x2, y2). The tool will calculate the slope and the y-intercept of the line based on the formula above. The calculator will show you the chart based on your input as well. You can also download the result in PDF filetype.

The general formula for slope-intercept form is , where represents the slope of the line, and represents the -value of the line’s -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 -axis.

✨ 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 -value of the -intercept and write the equation in slope-intercept form.

What is Standard Form?

The general formula for the standard form of a linear equation is , where , , and are all integers.

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

What is Point-Slope Form?

The general formula for the point-slope form of a linear equation is , where represents the slope of a line that contains the point (, ).

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

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