SOLUTION: Find the equation of the line through the given pair of points in standard form using only integers? (-4,-1) and (5,8)

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Question 133213: Find the equation of the line through the given pair of points in standard form using only integers?
(-4,-1) and (5,8)
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 (-4,-1) and (5,8)

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 (-4,-1) and is the second point (5,8))

m=%288--1%29%2F%285--4%29 Plug in y%5B2%5D=8,y%5B1%5D=-1,x%5B2%5D=5,x%5B1%5D=-4 (these are the coordinates of given points)

m=+9%2F9 Subtract the terms in the numerator 8--1 to get 9. Subtract the terms in the denominator 5--4 to get 9


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=%281%29%28x--4%29 Plug in m=1, x%5B1%5D=-4, and y%5B1%5D=-1 (these values are given)


y%2B1=%281%29%28x--4%29 Rewrite y--1 as y%2B1


y%2B1=%281%29%28x%2B4%29 Rewrite x--4 as x%2B4


y%2B1=x%2B%281%29%284%29 Distribute 1

y%2B1=x%2B4 Multiply 1 and 4 to get 4

y=x%2B4-1 Subtract 1 from both sides to isolate y

y=x%2B3 Combine like terms 4 and -1 to get 3
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Answer:


So the equation of the line which goes through the points (-4,-1) and (5,8) is:y=x%2B3

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=3

Notice if we graph the equation y=x%2B3 and plot the points (-4,-1) and (5,8), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=x%2B3 through the points (-4,-1) and (5,8)

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