How Do You Find Intercepts of a Linear Equation?

The intercepts of a linear equation like

2x + 4y = 8

 are easy to find. Often mistakes are made when we don’t pay careful attention to the graph.

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 Typically, students understand that a variable needs to be set to zero.

But which one? The red box above shows how to find the y intercept by setting x = 0. This results in y = 0 and the ordered pair (0, 2). Notice that since we set x = 0, the ordered pair has a zero for its x value.

In the green box, the x intercept is found by setting y = 0 in the equation. This gives x = 4 and the ordered pair (4, 0).

This seems a little strange at first…to find where a graph crosses one of the axes, you set the other variable equal to zero. It seems like the opposite of what you should do. However, in this case it is the opposite that we must do. On the vertical axis, the intercepts is located at zero horizontally. Similarly, the intercept is located at at 0 vertically on the horizontal axis.  We need to ignore what seems easy and focus on the graph in depth.

This “ignoring what is easy” effect was demonstrated by George Costanza in an episode of Seinfeld.