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Equation of a Line

Q: What is the equation of a line?

A: The equation of a line is y=mx+b, where

m = slope

b = y-intercept

Q: What is slope?

A: The slope of a line is a measure of how steep the line is. A larger slope means that the line is steeper, while a smaller slope corresponds to a flatter line.

The equation for slope is:

Slope Equation
So essentially, slope is just the change in y divided by the change in x.

Slope Graphic

Let’s look at a graph with three different lines. Note that the green line has the largest slope, while the blue line has the smallest slope.

Slopes of three lines

Q: What is the y-intercept?

A: In the equation of a line, y=mx+b, the y-intercept is b. It is the y-value where the line crosses the y-axis.

Using the same three lines, let’s find their y-intercepts.

y-intercepts of three lines

Lastly, let’s look at the same three lines with their equations in y=mx+b form.

Equations of three lines

Any line is defined by just two pieces of information: the slope, m, and the y-intercept, b.