SOLUTION: write an equation of the line that passes through each pair of points #7 (5,1),(8,-2) #9 (5,2),(-7,-4)

Algebra ->  Linear-equations -> SOLUTION: write an equation of the line that passes through each pair of points #7 (5,1),(8,-2) #9 (5,2),(-7,-4)      Log On


   

Question 115124This question is from textbook Algebra 1
: write an equation of the line that passes through each pair of points
#7
(5,1),(8,-2)
#9
(5,2),(-7,-4) This question is from textbook Algebra 1

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
I'll do the first one to give you an idea how to do these types of problems


First lets find the slope through the points (5,1) and (8,-2)

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 (5,1) and is the second point (8,-2))

m=%28-2-1%29%2F%288-5%29 Plug in y%5B2%5D=-2,y%5B1%5D=1,x%5B2%5D=8,x%5B1%5D=5 (these are the coordinates of given points)

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


m=-1 Reduce

So the slope is
m=-1

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


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

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

y=-x%2B5%2B1 Add 1 to both sides to isolate y

y=-x%2B6 Combine like terms 5 and 1 to get 6
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Answer:


So the equation of the line which goes through the points (5,1) and (8,-2) is:y=-x%2B6

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1 and the y-intercept is b=6

Notice if we graph the equation y=-x%2B6 and plot the points (5,1) and (8,-2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=-x%2B6 through the points (5,1) and (8,-2)

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