# Matching a Graph of a Straight Line with Its Equation

## Objectives

After reviewing this unit you will be able to:

• Match a graph with its equation.

## Matching Using Slope and y-intercept

Another skill you need is the ability to match an equation with its graph. One way to do this is to use the information you have about the equation of a straight line.

 In the last unit you learned that the equation of a line is given on the right. One way to match an equation of a straight line with the graph of a straight line is to use the slope and y-intercept. Here is an example of the graph of an equation. Below is the graph of the equation y = 2 x + 10.

 We can prove to ourselves that this is the graph of the equation y = 2 x + 10 by checking for two things: Does the line cross the y-axis at 10? Is the slope of the line on the graph 2? By looking at the graph you should notice that the line does cross the y-axis at point A, (0, 10). Now, you need to just check for the slope. You can do this by using the points B, (10, 30), and C, (20, 50). Using these points, the slope is: Since the slope is found to be two, the graph of the line and the equation of the line match. Let's take a look at an example.

### Example

 Consider the following graph at the right. Is the equation of the line shown in the graph above: y = 4 - 6 x, or y = 6 - (1/4) x? The things we need to check for are: The y-intercept. The slope of the line on the graph. • The y-intercept.

If you examine the graph, you should notice that the line crosses the y-axis at the point (0, 6). Therefore, the y-intercept is 6.

• The slope of the line on the graph.

Using the points (4, 5) and (12, 3) from the graph (NOTE: you can use any two points from the graph), the slope is calculated to be: So the slope of the line is (-1/4)

Given this, the equation of the line must be y = 6 - (1/4) x.

You are now ready to try a practice problem. Move on to the first practice for this unit. If you have already completed the first problem try the additional pratice before moving on to the summary for this part of the tutorial.    [practice] [additional practice] [table of contents] [next unit]