Question 78569: Can you tell and explain the equation of the line with given slope and y-intercept. Then graph each line using
the slope and y-intercept.
Slope: - 3/4; y-intercept: (0, 8)
Answer by bucky(2189)   (Show Source):
You can put this solution on YOUR website! Given the following information for an equation and its graph:
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Slope: - 3/4; y-intercept: (0, 8)
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The slope-intercept equation says that the equation is of the form:
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y = mx + b
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in which m is the slope and b is the point at which the graph crosses the y axis.
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All you have to do now is to substitute the given values of the slope and y intercept
into the slope intercept equation. When you make the two substitutions you get:
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y = (-3/4)x + 8
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You already know one point on the graph. That point is (0, 8) the point at which the
graph crosses the y-axis. You can plot that point by going +8 units up the y-axis
and putting a dot there.
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Now you can pick a convenient value for x, substitute it into the equation and find the
corresponding value of y. Let's pick x = 4 and substitute it into the equation to get:
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y = (-3/4)(4) + 8
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Multiply out (-3/4) times 4 and you get -3. This makes the equation become:
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y = -3 + 8
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and adding the terms on the right you find that y = +5 when x = +4. Therefore, you know
that (4, 5) is another point on the graph.
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Just as a check, let's find one more point on the graph. Suppose we let x = 8 and
substitute that value into the equation. If we do that we get:
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y = (-3/4)*8 + 8 = -6 + 8 = +2
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Therefore, we know that when x = 8, y = 2 so the point (8, 2) should be on the graph.
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Plot the three points (0, 8), (4, 5) and (8, 2) and draw a straight line that runs
through all three of these points. That should be the graph and it should look somewhat
like this:
.
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Hope this helps you to understand the problem and how to solve it.
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