How to Use Slope to Figure Out a Point on a Graph

The steeper the graph, the larger the slope.

The slope of a line represents the rate of change. If the slope is large, the line increases quickly. A smaller slope represents a flatter line. A negative slope means the line is going down. In order to use slope to find a point on the graph, you need to also know the y-intercept of the line. The y-intercept is the point at which the line crosses the y-axis.

Things You'll Need

• Calculator

Instructions

1. Plug the slope and y-intercept of the line into the following equation, where b is the y-intercept and m is the slope: y = mx + b. For example, if the slope of the line equals -2 and the y-intercept equals 4, your equation would be y = -2x + 4.

2. Plug in either the x-coordinate or the y-coordinate of the desired point. For example, if you wanted to find the point on the graph where the x-coordinate equals 6, plug in 6 for x in the equation to get y = -2(6) + 4.

3. Simplify the expression to find the other coordinate of the point on the graph. Finishing this example, simplify the equation by multiplying -2 by 6 to get -12 and adding 4 to find when the x-coordinate equals 6, the y-coordinate equals -8.

References

• Purple Math: Using Slope and y-Intercept to Graph Lines
• Math Open Reference: Slope of a Line