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Question 249498: Write th slope intercept form of an equation of the line that passes through the point (4,4) and has the slope m=5.
Answer by oberobic(2304)   (Show Source):
You can put this solution on YOUR website! Slope-intercept form is: y = mx+b
m = 5 (given)
Since the slope = rise/run = change in 'y' divided by change in 'x', m=5 tells us that for a change of 1 in x we have a change of 5 in y.
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One point is given: (4,4)
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Substituting back into the equation, we have...
4 = 5(4) + b
4 = 20 + b
-16 = b
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So the intercept appears to be -16.
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The resulting equation is:
y = 5x - 16
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Is it true for (4,4)?
Yes.
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Is it true for another point?
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Well, we can define another point based on knowing the slope.
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m=5 means when we add 1 to x, the result is 5 being added to y.
Let's do just that: (4+1, 4+5) would do so.
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Now we have two points: (4,4) and (5,9).
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Does y= 5x -16 work for the point (5,9)?
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9 = 5(5) - 16
9 = 25 - 16
True.
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We also are informed by graphing the line.
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Looking at the graph reminds us to check the point ( ?, 0).
0 = 5x - 16
5x = 16
x = 3.2
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Inspecting the graph shows that looks right.
Done.
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