Question 49181: Graph using the intercept method: x + 3y = 6.
Answer by Born2TeachMath(20)   (Show Source):
You can put this solution on YOUR website! The intercept method means determining where the graph of the line "intercepts" the x-axis and the y-axis. So, how do you find an intercept? Well, what do you know about a point that "intercepts" the x-axis (for example?) If a point is on the x-axis, then the y-coordinate of that point must be zero! (otherwise the point would be above or below the x-axis, and not on it.) Similarly, if a point is on the y-axis, then the x-coordinate of that point must be zero! (otherwise the point would be left or right of the y-axis, and not on it.)
Therefore, the important point to realize is that if you're looking for an intercept, then the opposite letter must be zero!
So, for your equation: x + 3y = 6, we do the following -
To find the x-intercept, set y = 0, and solve for x:
x + 3(0) = 6
x + 0 = 6
x = 6. So the x-intercept is the point (6, 0)
Doing the same for the y-intercept (x = 0)
0 + 3y = 6
y = 6/(3)
y = 2. So the y-intercept is the point (0, 2)
Finally, once you have the two points, plot them on the graph paper, and then just draw a line between the two points.
The intercept method is great when an equation is given in what is known as STANDARD FORM, such as Ax + By = C. It's a lot easier than converting to y = mx + b form, especially if A and B divide into C easily, like yours did.
Good luck, and I hope this helps. I use it all of the time to sketch graphs in word problems.
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