SOLUTION: what is an equation in slope intercept-form for a line passing through(3,4)And (5,8)?

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Question 111347: what is an equation in slope intercept-form for a line passing through(3,4)And (5,8)?
Answer by jim_thompson5910(35256) 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 (3,4) 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: (x%5B1%5D,y%5B1%5D) is the first point (3,4) and (x%5B2%5D,y%5B2%5D) is the second point (5,8))


m=%288-4%29%2F%285-3%29 Plug in y%5B2%5D=8,y%5B1%5D=4,x%5B2%5D=5,x%5B1%5D=3 (these are the coordinates of given points)


m=+4%2F2 Subtract the terms in the numerator 8-4 to get 4. Subtract the terms in the denominator 5-3 to get 2




m=2 Reduce



So the slope is

m=2





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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-4=%282%29%28x-3%29 Plug in m=2, x%5B1%5D=3, and y%5B1%5D=4 (these values are given)



y-4=2x%2B%282%29%28-3%29 Distribute 2


y-4=2x-6 Multiply 2 and -3 to get -6%2F1. Now reduce -6%2F1 to get -6

y=2x-6%2B4 Add 4 to both sides to isolate y


y=2x-2 Combine like terms -6 and 4 to get -2

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Answer:



So the equation of the line which goes through the points (3,4) and (5,8) is:y=2x-2


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


Notice if we graph the equation y=2x-2 and plot the points (3,4) and (5,8), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=2x-2 through the points (3,4) and (5,8)


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