Question 282706
y = mx+b is slope-intercept form, where
m = slope
b = y-intercept (defined by x=0)
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Two points can be used to draw a line.
(-5,2) and (4,1)
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You also can determine the slope by computing the rise over the run.
rise = change in y = y<sub>2</sub> - y<sub>1</sub>
run = change in x = x<sub>2</sub> - x<sub>1</sub>
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We can define either point what we want, but we have to keep consistent.
(x<sub>1</sub>, y<sub>1</sub>) = (-5, 2)
(x<sub>2</sub>, y<sub>2</sub>) = (4, 1)
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rise = 1-2 = -1
run = 4 -(-5) = 4+5 = 9
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So,
m = -1/9
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That means y= -1/9x + b
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Now we have to compute 'b' to ensure it goes through the points given.
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We know that when x=4, y=1
Substituting, we find 'b'
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1 = -1/9*4 + b
1 + 4/9 = b
9/9 + 4/9 = b
13/9 = b
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So, we now have the equation:  y = -1/9x + 13/9
Slope = -1/9
y-intercept = (0, 13/9)
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The x-intercept occurs where y=0, so we can solve by substitution again.
0 = -1/9x + 13/9
The obvious answer is x=13, so the point is (13,0).
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Graphing is a good way to check your work.
{{{graph(500,500,-10,15,-5,5,-1/9*x+13/9)}}}
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