SOLUTION: What is the equation in slope intercept form for the line through each pair of points? (-3,1) and (2,4) I think the slope is 3/5... so I'm thinking it's y=3/5x + some number.

Algebra ->  Linear-equations -> SOLUTION: What is the equation in slope intercept form for the line through each pair of points? (-3,1) and (2,4) I think the slope is 3/5... so I'm thinking it's y=3/5x + some number.      Log On


   

Question 102872: What is the equation in slope intercept form for the line through each pair of points?
(-3,1) and (2,4)
I think the slope is 3/5... so I'm thinking it's y=3/5x + some number... but I'm having problems getting the rest. Help would be much appreciated.
Answer by edjones(8007) 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 (-3,1) and (2,4)


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 (-3,1) and (x%5B2%5D,y%5B2%5D) is the second point (2,4))


m=%284-1%29%2F%282--3%29 Plug in y%5B2%5D=4,y%5B1%5D=1,x%5B2%5D=2,x%5B1%5D=-3 (these are the coordinates of given points)


m=+3%2F5 Subtract the terms in the numerator 4-1 to get 3. Subtract the terms in the denominator 2--3 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-1=%283%2F5%29%28x--3%29 Plug in m=3%2F5, x%5B1%5D=-3, and y%5B1%5D=1 (these values are given)



y-1=%283%2F5%29%28x%2B3%29 Rewrite x--3 as x%2B3



y-1=%283%2F5%29x%2B%283%2F5%29%283%29 Distribute 3%2F5


y-1=%283%2F5%29x%2B9%2F5 Multiply 3%2F5 and 3 to get 9%2F5

y=%283%2F5%29x%2B9%2F5%2B1 Add 1 to both sides to isolate y


y=%283%2F5%29x%2B14%2F5 Combine like terms 9%2F5 and 1 to get 14%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 (-3,1) and (2,4) is:y=%283%2F5%29x%2B14%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=14%2F5


Notice if we graph the equation y=%283%2F5%29x%2B14%2F5 and plot the points (-3,1) and (2,4), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%283%2F5%29x%2B14%2F5 through the points (-3,1) and (2,4)


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