Slope Intercept Form Calculator with Two Points

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

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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 $$$x_{1} = -1$$$, $$$y_{1} = 5$$$, $$$x_{2} = 3$$$, $$$y_{2} = 7$$$.

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.