# Line Calculator

This calculator will find the equation of a line (in the slope-intercept, point-slope, and general forms) given two points or the slope and one point, with steps shown.

Related calculators: Slope Calculator, Parallel and Perpendicular Line Calculator

Choose type:

Enter two points or

Point 1: (, )

Point 2: (, )

Enter a slope and a point or

Slope:

Point: (, )

If slope is infinite or undefined, write inf.
If you need to find a parallel or perpendicular line, use the parallel and perpendicular line calculator.
To find a slope, use the slope calculator.

If the calculator did not compute something or you have identified an error, or you have a suggestion/feedback, please write it in the comments below.

## Solution

Your input: find the equation of a line given two points $P=\left(-4, 7\right)$ and $Q=\left(1, 2\right)$.

The slope of a line passing through the two points P=(x_1, y_1) and Q=(x_2, y_2) is given by m=(y_2-y_1)/(x_2-x_1).

We have that $x_1=-4$, $y_1=7$, $x_2=1$, $y_2=2$.

Plug the given values into the formula for slope: $m=\frac{\left(2\right)-\left(7\right)}{\left(1\right)-\left(-4\right)}=\frac{-5}{5}=-1$.

Now, the y-intercept is b=y_1-m*x_1 (or b=y_2-m*x_2, the result is the same).

$b=7-\left(-1\right) \cdot \left(-4\right)=3$.

Finally, the equation of the line can be written in the form y=mx+b.

$y=-x+3$.

The slope of the line is $m=-1$.
The equation of the line in the slope-intercept form is $y=-x+3$.
The equation of the line in the point-slope form is $y - 7 = - (x + 4)$.
The equation of the line in the point-slope form is $y - 2 = - (x - 1)$.
The general equation of the line is $x + y - 3 = 0$.