Finding the Equation of a Line

You may be given a graph and asked a question that requires know the equation of a line.

Example:

Where will the line shown in the graph above intersect the x-axis?

A) -5.5

B) -5

C) -4.5

D) -4

Strategy:

To find the equation of a line from a graph, you have two options:

  1. 2 coordinate method: Find two coordinate points, and then use those coordinate points to find the equation of the line.  You should have practiced this in the previous unit.
  2. Graph method: The second method involves visually determining the slope and y-intercept.

Since the slope of a line is simply rise over run, we can trace with our pencils–starting at the y-intercept of the line–up 2 units and over 1 unit (note the different scales for the grid lines on the graph for the x and y axes – this is a common SAT trick).  Therefore, our slope is \(\frac21\).  Now by circling the point where the line intersects with the y-axis, we can determine that the y-intercept, or \(b\), is positive 10.  We now have our linear equation:

$$y=2x+10$$

The question asks us where the line will intersect with the x-axis.  Where a line crosses the x-axis, the y values will always be zero, so we plug zero into our equation and solve for x:

$$0=2x+10\\-10=2x\\x=-5$$

The answer is B).

Traps

As noted in the example, watch out for different scales on the axes, or gridlines being two units instead of one as you might expect.