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Question 110289: graph f(x)=-3x-2
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! What you are asked to graph is the function:
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f(x) = -3x - 2
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To get it into a little more conventional form, replace f(x) by y to get:
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y = -3x - 2
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One way to graph this is to assign "convenient" values to x or y and determine the corresponding
value of the other variable. Then plot the point. Two points will be enough to draw this
line graph, and a third point might be a good idea ... just to make sure the three points all
lie on one straight line. If one of the points is off the line, you know something is wrong.
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Let's do an easy point ... let's assign x the value of zero. When x equals zero, the term
-3x is equal to zero and therefore drops from the equation. This reduces the equation to
y = -2. So when x = 0, then y = -2. This tells you that the point (0, -2) is on the graph.
(Note that since x = 0, the point is at -2 on the y-axis.)
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Although it is not as nice, suppose we assign y the value of zero. If we do, the equation
becomes:
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0 = -3x - 2
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We can get rid of the -3x on the right side by adding +3x to both sides. The result of
this addition is that it changes the equation to:
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3x = -2
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Then you can solve for x by dividing both sides by 3 to get:
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x = -2/3
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This tells you that the point (-2/3, 0) is on the graph. Note that this point is located at
-2/3 on the x-axis because points that have zero as their y-value are on the x-axis.
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Finally, determine one more point. Return to the original equation:
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y = -3x - 2
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We can pick any number for x. Suppose we let x = -2. If we substitute -2 for x the equation
becomes:
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y = -3(-2) - 2 = +6 - 2 = +4
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This tells you that the point (-2, +4) is also on the graph. Plot the three points on a
coordinate system and draw a straight line through them. Your graph should look like this:
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You should be able to see from this graph that the three points we found are all on this line.
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Hope this helps you to understand one method of determining the graph of a linear equation.
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