# 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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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 $y = b + m x$:

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

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.