Question 81543: Graph f(x) = –3x – 2.
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Substitute y for f(x) to get:
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y = -3x - 2
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This equation is in the slope-intercept form:
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y = mx + b
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in which m (the multiplier of x) is the slope of the graph and b is the value on the y-axis
where the graph crosses.
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So for a start, you can tell by comparing the given equation to the slope-intercept form
that b (the crossing point on the y-axis) is -2. On your coordinate system put a dot at
-2 on the y-axis.
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Next, again by comparing the given equation with the slope-intercept form, you can tell
that the slope is -3. The minus sign tells you that the graph slants downward as you move
to the right along the x-axis. For every 1 unit you move horizontally to the right, the
graph goes down 3 units. So put your pencil tip on the one point you know, that point being
-2 on the y-axis. Then move your pencil tip 1 unit horizontally to the right and stop. From
that location move your pencil point vertically down 3 units in the y-direction. Stop there
and mark that point. It is on the graph. (As a check, the point should be (1, -5).
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As another check, you can go back to the given equation and set y equal to zero. The corresponding
value of x will be on the x-axis because points along the x-axis all have zero as their
y-value. When you set y = 0 in the given equation, it becomes:
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0 = -3x - 2
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Add 2 to both sides to get rid of the -2 on the right side. When you do, the equation
becomes:
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2 = -3x
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Finally divide both sides by -3 to solve for x. When you do that division you get:
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2/(-3) = x
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which is the same as:
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x = -2/3
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So when x is -2/3 then y is zero. So another point on the graph is (-2/3, 0). You can
plot it and see if it lies on the graph. You should be able to take a straight edge and
lay it along all three dots you have found and be able to extend a line through all three
of the dots. That line is the graph of y = -3x - 2.
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Note that you can assign other values to x, and use the given equation to find corresponding
values of y if you want to get more points for your graph. For example, set x equal to
-2. The equation becomes:
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y = -3(-2) - 2 = 6 - 2 = 4
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So another point on your graph is (-2, 4)
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When you get done your graph should look like:
.
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Hope this helps you understand graphs for linear equations a little more.
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