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Question 550022: Find an equation in slope-intercept form passing through the points (-6.2,18.1) and (-3.4,18.1).
Found 2 solutions by Alan3354, bucky:
Answer by Alan3354(69443)   (Show Source):
Answer by bucky(2189)  (Show Source):
You can put this solution on YOUR website! This one might be a little confusing to you.
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Normally, the slope intercept form is:
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in which m, the multiplier of x, is the slope and b is the value on the y-axis where the linear graph of the equation crosses the y-axis.
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The slope is normally computed by dividing the change in x from the two given points into the corresponding change in y. In this case, note that in the two points that are given, x goes from -6.2 in one of the points to - 3.4 in the other. Subtracting the -6.2 from -3.4 results in a difference of +2.8. So in finding the slope, +2.8 is what we'll be dividing into the corresponding change in the y values of the two points.
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But, what is the change in y? The value of y in the first point is 18.1 and the value of y in the second point is also 18.1. The difference in these two values is zero. So while x went 2.8 units toward the right (the run from -6.1 to -3.4) the value of y stayed the same and, therefore, the rise was zero. Dividing 2.8 into zero results in a slope of zero.
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Return to the the slope-intercept form for the equation. When you substitute zero for the slope the equation becomes:
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The multiplication by zero makes the x term disappear and we are left with:
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Now all we have to realize is that y never changes regardless of what value we choose for x. For this problem the value of y is always 18.1 and the graph is a horizontal line (parallel to the x-axis) that crosses the y-axis at +18.1. This means that b is 18.1 and the slope intercept equation is simply:
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That's all there is to it. Whenever you see a slope intercept form that says simply y equals a constant, you should picture a graph that is a horizontal line and crosses the y-axis at the value of the constant.
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Hope this helps you to understand the "trick" in this problem and what it means.
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