SOLUTION: Find an equation of the line that passes through the points (-1, -2) and (4, -5)

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Question 954301: Find an equation of the line that passes through the points (-1, -2) and (4, -5)
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (-1,-2) and (4,-5)


m=%28y%5B2%5D-y%5B1%5D%29%2F%28x%5B2%5D-x%5B1%5D%29 Start with the slope formula (note: (x%5B1%5D,y%5B1%5D) is the first point (-1,-2) and (x%5B2%5D,y%5B2%5D) is the second point (4,-5))


m=%28-5--2%29%2F%284--1%29 Plug in y%5B2%5D=-5,y%5B1%5D=-2,x%5B2%5D=4,x%5B1%5D=-1 (these are the coordinates of given points)


m=+-3%2F5 Subtract the terms in the numerator -5--2 to get -3. Subtract the terms in the denominator 4--1 to get 5



So the slope is

m=-3%2F5





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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 (x%5B1%5D,y%5B1%5D) is one of the given points


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


y--2=%28-3%2F5%29%28x--1%29 Plug in m=-3%2F5, x%5B1%5D=-1, and y%5B1%5D=-2 (these values are given)



y%2B2=%28-3%2F5%29%28x--1%29 Rewrite y--2 as y%2B2



y%2B2=%28-3%2F5%29%28x%2B1%29 Rewrite x--1 as x%2B1



y%2B2=%28-3%2F5%29x%2B%28-3%2F5%29%281%29 Distribute -3%2F5


y%2B2=%28-3%2F5%29x-3%2F5 Multiply -3%2F5 and 1 to get -3%2F5

y=%28-3%2F5%29x-3%2F5-2 Subtract 2 from both sides to isolate y


y=%28-3%2F5%29x-13%2F5 Combine like terms -3%2F5 and -2 to get -13%2F5 (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 (-1,-2) and (4,-5) is:y=%28-3%2F5%29x-13%2F5


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-3%2F5 and the y-intercept is b=-13%2F5


Notice if we graph the equation y=%28-3%2F5%29x-13%2F5 and plot the points (-1,-2) and (4,-5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-3%2F5%29x-13%2F5 through the points (-1,-2) and (4,-5)


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