B. Determining an Equation for a Linear Relation

By using known relationships between the graph and the equation of a linear relation, the equation of a linear relation can be determined from its graph.

Example 1

Determine an equation that represents the linear relation shown in the graph.

By determining the slope and the y-intercept of the graph of the relation, an equation can be determined.

Pick two points on the graph and determine the slope. Here, (0,2) and (6,4) are used.

The y-intercept can be determined by inspection, so b = 2.

Use the slope and y-intercept to write the equation.

The relationships between the graph of a relation and its equation in slope-intercept form can also be used to quickly sketch the graph when the equation is known. Plot the y-intercept and then use the slope to determine another point on the graph. Draw a line to connect the two points.

 Only two points are required to graph a linear relation. Determining a third point helps to catch errors. If a linear equation is used to determine three points that don't line up on a graph, you will know you've made an error.