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:**

*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.***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 identifying 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).

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.

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