You can
put this solution on YOUR website!I presume that y = -3 refers to the y-axis intercept.
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Given the slope and the y-axis intercept, you can write the equation of the line using the
slope-intercept form for an equation. This form is:
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y = mx + b
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where m is the slope and b is the y-axis intercept of the graph. Substituting the slope of +2
and the intercept of -3 for m and b respectively gives you the equation for the graph as:
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y = 2x - 3
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Using this equation you can now assign values to x and compute the corresponding values
for y. Then plot these points on the graph and you can connect the points with a straight
line that extends through them. For example, you know from the problem that the y-axis intercept
is -3 and that any point on the y-axis has an x value of 0. So one of the points on the
graph is (0, -3).
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You can get another point on the graph using the slope intercept equation that we developed.
Let's just say that x equals 5. Substitute this value for x in the equation and you have:
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y = 2(5) - 3 = 10 - 3 = 7
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From this we see that when x = 5, the corresponding value for y is 7. So the point
(5, 7) is on the graph. Plot it. You now have the two points (0, -3) and (5, 7) and this
is enough information to make the graph. Just extend a straight line through these two
points and that is the graph. However, it's usually a good idea to find at least one or two
more points just to make sure that they line up on the graph also ... just to make sure
you haven't made an error someplace. Why not assume that x = -5. Plugging this value into
the equation results in:
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y = 2(-5) - 3 = -10 - 3 = -13
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This tells us that the point (-5, -13) also is on the graph. Plot it and make sure that
it is in line with the other two points. You can select more values for x and determine
the corresponding values of y just to make sure they also are on the line. This is one
way to graph the equation.
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Another way is to recognize what the slope means. Since the slope is +2 that means that
for every unit you move horizontally in the direction of increasing x (that is move 1
unit horizontally to the right) the value of y will go up by +2 units. You know that the
point -3 on the y-axis is on the graph. Put your pencil point at that spot. Then move your
pencil point 1 unit horizontally to the right. When you have done that, move your pencil
point vertically up 2 units. Stop there and mark the spot. That point will be on the graph.
You can continue this process ... one horizontally to the right then two vertically
up. Mark that point. Starting there, go 1 to the right then up 2. And again. This will
give you a series of points that are on the graph.
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When you get done your graph should look like this:
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Hope this helps you to understand this problem a little better.
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