SOLUTION: I can figure out how to find a slope of a line, but in the slope intercept form, I get confused. Here is my problem I am having trouble on. Find the equation, in slope-interce

Algebra ->  Graphs -> SOLUTION: I can figure out how to find a slope of a line, but in the slope intercept form, I get confused. Here is my problem I am having trouble on. Find the equation, in slope-interce      Log On


   

Question 114348: I can figure out how to find a slope of a line, but in the slope intercept form, I get confused. Here is my problem I am having trouble on.
Find the equation, in slope-intercept form, of the line that passes through the points (5, 6) and (-7, 3).
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 (5,6) 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: (x%5B1%5D,y%5B1%5D) is the first point (5,6) and (x%5B2%5D,y%5B2%5D) is the second point (-7,3))


m=%283-6%29%2F%28-7-5%29 Plug in y%5B2%5D=3,y%5B1%5D=6,x%5B2%5D=-7,x%5B1%5D=5 (these are the coordinates of given points)


m=+-3%2F-12 Subtract the terms in the numerator 3-6 to get -3. Subtract the terms in the denominator -7-5 to get -12




m=1%2F4 Reduce



So the slope is

m=1%2F4





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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-6=%281%2F4%29%28x-5%29 Plug in m=1%2F4, x%5B1%5D=5, and y%5B1%5D=6 (these values are given)



y-6=%281%2F4%29x%2B%281%2F4%29%28-5%29 Distribute 1%2F4


y-6=%281%2F4%29x-5%2F4 Multiply 1%2F4 and -5 to get -5%2F4

y=%281%2F4%29x-5%2F4%2B6 Add 6 to both sides to isolate y


y=%281%2F4%29x%2B19%2F4 Combine like terms -5%2F4 and 6 to get 19%2F4 (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 (5,6) and (-7,3) is:y=%281%2F4%29x%2B19%2F4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1%2F4 and the y-intercept is b=19%2F4


Notice if we graph the equation y=%281%2F4%29x%2B19%2F4 and plot the points (5,6) and (-7,3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%281%2F4%29x%2B19%2F4 through the points (5,6) and (-7,3)


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