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.

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`.

$$$y=-x+3$$$.

Answer:

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 $$$x + y - 3 = 0$$$.