SOLUTION: Find an equation in slope-intercept form passing through the points (2,5) and (7,-3). Any help with this equation would be appreciated. Thank you.

Algebra ->  Graphs -> SOLUTION: Find an equation in slope-intercept form passing through the points (2,5) and (7,-3). Any help with this equation would be appreciated. Thank you.      Log On


   

Question 142430: Find an equation in slope-intercept form passing through the points (2,5) and
(7,-3). Any help with this equation would be appreciated. Thank you.
Found 2 solutions by checkley77, jim_thompson5910:
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(2,5) & (7,-3)
First we find the slope (m) (y2-y1)/(x2-x1)
m=(-3-5)/(7-2)
m=-8/5 is the slope.
now we replace the x & y terms with one set of points & solve for the y intercept (b) in the equation [Y=mX+b]
5=-8/5*2+b
5=-16/5+b
5+16/5=b
(25+16)/5=b
41/5=b the y intercept.
Thus the equation is:
y=-8x/5+41/5
+graph%28+300%2C+200%2C+-6%2C+10%2C+-10%2C+10%2C+-8x%2F5+%2B41%2F5%29+ (graph 300x200 pixels, x from -6 to 10, y from -10 to 10, -8x/5 +41/5).

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 (2,5) and (7,-3)

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 (2,5) and is the second point (7,-3))

m=%28-3-5%29%2F%287-2%29 Plug in y%5B2%5D=-3,y%5B1%5D=5,x%5B2%5D=7,x%5B1%5D=2 (these are the coordinates of given points)

m=+-8%2F5 Subtract the terms in the numerator -3-5 to get -8. Subtract the terms in the denominator 7-2 to get 5

So the slope is
m=-8%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 is one of the given points

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

y-5=%28-8%2F5%29%28x-2%29 Plug in m=-8%2F5, x%5B1%5D=2, and y%5B1%5D=5 (these values are given)


y-5=%28-8%2F5%29x%2B%28-8%2F5%29%28-2%29 Distribute -8%2F5

y-5=%28-8%2F5%29x%2B16%2F5 Multiply -8%2F5 and -2 to get 16%2F5

y=%28-8%2F5%29x%2B16%2F5%2B5 Add 5 to both sides to isolate y

y=%28-8%2F5%29x%2B41%2F5 Combine like terms 16%2F5 and 5 to get 41%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 (2,5) and (7,-3) is:y=%28-8%2F5%29x%2B41%2F5

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-8%2F5 and the y-intercept is b=41%2F5

Notice if we graph the equation y=%28-8%2F5%29x%2B41%2F5 and plot the points (2,5) and (7,-3), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-8%2F5%29x%2B41%2F5 through the points (2,5) and (7,-3)

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