Linear and Quadratic Functions: Writing and Graphing Linear Functions

Writing a Linear Equation

Man sitting at desk thinking, in front of chalkboard

When asked to write an equation of a linear function, you can be given a few different pieces of information.

You may be given two points on a line and then asked to find the equation of the line that goes through these two points. For example, find the equation of a line that goes through points (3, 5) and (2, 4). The first step is to find the slope.

m equal to four minus five divided by two minus three equal to negative one divided by negative one equals one

Using the slope-intercept form of a linear equation, y = mx + b, you can now plug in the slope.

y = 1x + b
y = x + b

Now you need to find the y-intercept, or b, of the equation. Pick one of the points to plug back into the equation and then solve for b. Let’s work with (3, 5).

y = x + b
5 = 3 + b
b = 2

Now you can write the final equation, y = x + 2.