SOLUTION: 1. Find the slope of the line that passes through the points (-4, 1) and (3, 5)

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Question 145479:
1. Find the slope of the line that passes through the points (-4, 1) and (3, 5)


Answer by vleith(2983) 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 (-4,1) and (3,5)


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


m=%285-1%29%2F%283--4%29 Plug in y%5B2%5D=5,y%5B1%5D=1,x%5B2%5D=3,x%5B1%5D=-4 (these are the coordinates of given points)


m=+4%2F7 Subtract the terms in the numerator 5-1 to get 4. Subtract the terms in the denominator 3--4 to get 7



So the slope is

m=4%2F7





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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=%284%2F7%29%28x--4%29 Plug in m=4%2F7, x%5B1%5D=-4, and y%5B1%5D=1 (these values are given)



y-1=%284%2F7%29%28x%2B4%29 Rewrite x--4 as x%2B4



y-1=%284%2F7%29x%2B%284%2F7%29%284%29 Distribute 4%2F7


y-1=%284%2F7%29x%2B16%2F7 Multiply 4%2F7 and 4 to get 16%2F7

y=%284%2F7%29x%2B16%2F7%2B1 Add 1 to both sides to isolate y


y=%284%2F7%29x%2B23%2F7 Combine like terms 16%2F7 and 1 to get 23%2F7 (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 (-4,1) and (3,5) is:y=%284%2F7%29x%2B23%2F7


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=4%2F7 and the y-intercept is b=23%2F7


Notice if we graph the equation y=%284%2F7%29x%2B23%2F7 and plot the points (-4,1) and (3,5), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%284%2F7%29x%2B23%2F7 through the points (-4,1) and (3,5)


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