Lines and the Coordinate Plane: Graphing the Equation of a Line

Point-Slope Form

Depending on the given information, it can be useful to write the point-slope form of an equation. When you are given one point and the slope, this is the easiest form to use.

Point-Slope Form

y - y1 = m(x - x1)

Where m is the slope and (x1, y1) is a point on the line.


Example 1

Write the equation of the line through (4, -5) with a slope of negative three-fourths.

Simply substitute the given information into the given equation.

y minus y 1 equals m times the quantity x minus x 1, y minus negative 5 equals negative three-fourths times the quantity x minus 4, y plus 5 equals negative three-fourths times the quantity x minus 4

You can also use the point-slope form of an equation to help you to write the slope-intercept form of an equation.

Example 2

Write the equation of the line through (1, 2) and with a slope of -3 in slope-intercept form.

First, write the equation in point-slope form.

y - 2 = -3(x - 1)

Now, solve the equation for y.

y - 2 = -3(x - 1)

Apply the distributive property.

y - 2 = -3x + 3

y = -3x + 5

The equation is now in slope-intercept form.