140 Part 2: Into the Unknown
Quick Graphing
Making a table and plotting points will always get you a graph, but it can be a slow process.
There are two ways to get the graph quickly, and it’s good to know both, because the way the
equation is arranged will determine which method works better.
The first method uses the fact that a point on an axis will always have one coordinate that’s- Points on the x-axis have 0 as their y-coordinate, and points on the y-axis have 0 as their
x-coordinate. These points on the x-axis and y-axis are called intercepts, and the method is
called the intercept-intercept method.
To graph 3x – 4y = 12 by the intercept-intercept method, replace x with 0 and find y. 3(0) – 4y
= 12 becomes just -4y = 12, so y = -3. The point (0,-3) is the y-intercept. Go back to the original
equation and let y = 0. 3x – 4(0) = 12 becomes just 3x = 12 and x = 4. The x-intercept is (4,0).
Plot the x-intercept and the y-intercept, connect them, and extend to make the line 3x – 4y = 12.
Although it can be used for graphing any equation, the intercept-intercept method is best used
when the equation has the x and y terms on the same side and the constant on the other side. When
the equation is arranged that way, the arithmetic of finding the intercepts is usually simple.-6 -2 062
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