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Answer
To graph
, plot the points (3, 0) and (0, 3) and draw a line through them.
Solution
To graph the equation
, we can plot the points on the coordinate plane and draw a line through them.
Let’s find the x-intercept by setting
:
So, the x-intercept is at (3, 0).
Now, let’s find the y-intercept by setting
:
So, the y-intercept is at (0, 3).
Plotting these points on the coordinate plane, we can draw a line through them to represent the graph of the equation
.
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The Deep Dive
To graph the equation
, start by plotting the y-intercept at (0, 3) on the y-axis. Next, notice that the slope is -1, meaning for every one unit you move to the right on the x-axis, you move down one unit on the y-axis. From the point (0, 3), move right to (1, 2), and then to (2, 1), which gives you another point. Connect these points with a straight line, and you’ll have your graph!
If you’re new to graphing, remember to identify key points clearly. Also, a common mistake is trying to skimp on the scale; be sure to use consistent intervals on both axes. This keeps your graph tidy and makes it easier to plot future equations accurately!