Equation of a Line: Point-Slope Form

This math recipe will help you find the equation of a line, whose slope is given and which passes through a given point.

Easy

Approx. 1 min

Slope of the line: m

The point through which the line passes: (x₁, y₁)

To find the equation of the line, we’ll use the following:

(y – y₁) = m(x – x₁)

Example 1 Find the equation of a line whose slope is –3 and passes through (4, 2).

Solution To find the equation, we’ll use the above form directly.

y – 2 = –3(x – 4)

=> 3x + y – 14 = 0

The figure shows the line on the XY plane.

Example 2 Find the equation of a line whose slope is 0 and passes through (1, -3).

Solution To find the equation, we’ll use the above form directly.

(y – (-3)) = 0(x – 1)

=> y + 3 = 0

The figure shows the line on the XY plane.

Example 3 Find the equation of a line that makes an angle of 45° with the x-axis and passes through (-2, 3).

Solution To find the equation, first we’ll find the slope.

m = tan45° = 1

Now, let’s use the above form.

(y – 3) = 1(x – (-2))

=> x – y + 5 = 0

The figure shows the line on the XY plane.

That’s it for this recipe. Hope you found it helpful.

For more recipes, please visit www.doubleroot.in/recipes.

You can follow me on Instagram, Twitter, or Facebook to get all updates.