SOLUTION: write an equation for the line in slope-intercept form. Passing through (5,5) and (8,4)

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Question 115434: write an equation for the line in slope-intercept form.
Passing through (5,5) and (8,4)
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
First lets find the slope through the points (5,5) and (8,4)

m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: is the first point (5,5) and is the second point (8,4))

m=%284-5%29%2F%288-5%29 Plug in y%5B2%5D=4,y%5B1%5D=5,x%5B2%5D=8,x%5B1%5D=5 (these are the coordinates of given points)

m=+-1%2F3 Subtract the terms in the numerator 4-5 to get -1. Subtract the terms in the denominator 8-5 to get 3

So the slope is
m=-1%2F3

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Now let's use the point-slope formula to find the equation of the line:



------Point-Slope Formula------
y-y%5B1%5D=m%28x-x%5B1%5D%29 where m is the slope, and is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

y-5=%28-1%2F3%29%28x-5%29 Plug in m=-1%2F3, x%5B1%5D=5, and y%5B1%5D=5 (these values are given)


y-5=%28-1%2F3%29x%2B%28-1%2F3%29%28-5%29 Distribute -1%2F3

y-5=%28-1%2F3%29x%2B5%2F3 Multiply -1%2F3 and -5 to get 5%2F3

y=%28-1%2F3%29x%2B5%2F3%2B5 Add 5 to both sides to isolate y

y=%28-1%2F3%29x%2B20%2F3 Combine like terms 5%2F3 and 5 to get 20%2F3 (note: if you need help with combining fractions, check out this solver)


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Answer:


So the equation of the line which goes through the points (5,5) and (8,4) is:y=%28-1%2F3%29x%2B20%2F3

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1%2F3 and the y-intercept is b=20%2F3

Notice if we graph the equation y=%28-1%2F3%29x%2B20%2F3 and plot the points (5,5) and (8,4), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F3%29x%2B20%2F3 through the points (5,5) and (8,4)

Notice how the two points lie on the line. This graphically verifies our answer.