SOLUTION: Find the slope of the line through the given points. Also find the slope intercept form. Find the Y intercept and the X intercept for one of the points. (-7/5, 3/10) and (1/5, -1/

Algebra ->  Graphs -> SOLUTION: Find the slope of the line through the given points. Also find the slope intercept form. Find the Y intercept and the X intercept for one of the points. (-7/5, 3/10) and (1/5, -1/      Log On


   

Question 102458: Find the slope of the line through the given points. Also find the slope intercept form. Find the Y intercept and the X intercept for one of the points.
(-7/5, 3/10) and (1/5, -1/2)
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 (-7%2F5,3%2F10) and (1%2F5,-1%2F2)

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 (-7%2F5,3%2F10) and is the second point (1%2F5,-1%2F2))

m=%28-1%2F2-3%2F10%29%2F%281%2F5--7%2F5%29 Plug in y%5B2%5D=-1%2F2,y%5B1%5D=3%2F10,x%5B2%5D=1%2F5,x%5B1%5D=-7%2F5 (these are the coordinates of given points)

m=+%28-8+%2F+10%29%2F%288+%2F+5%29 Subtract (note: if you need help with subtracting or dividing fractions, check out this solver)



m=-1+%2F+2 Divide the fractions

So the slope is
m=-1+%2F+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 is one of the given points

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

y-3%2F10=%28-1+%2F+2%29%28x--7%2F5%29 Plug in m=-1+%2F+2, x%5B1%5D=-7%2F5, and y%5B1%5D=3%2F10 (these values are given)


y-3%2F10=%28-1+%2F+2%29%28x%2B7%2F5%29 Rewrite x--7%2F5 as x%2B7%2F5


y-3%2F10=%28-1%2F2%29x%2B%28-1%2F2%29%287%2F5%29 Distribute -1+%2F+2

y-3%2F10=%28-1%2F2%29x-7%2F10 Multiply -1+%2F+2 and 7%2F5 to get -7%2F10

y=%28-1%2F2%29x-7%2F10%2B3%2F10 Add 3%2F10 to both sides to isolate y

y=%28-1%2F2%29x-2%2F5 Combine like terms -7%2F10 and 3%2F10 to get -2%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 (-7%2F5,3%2F10) and (1%2F5,-1%2F2) is:y=%28-1%2F2%29x-2%2F5

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-1+%2F+2 and the y-intercept is b=-2%2F5

Notice if we graph the equation y=%28-1%2F2%29x-2%2F5 and plot the points (-7%2F5,3%2F10) and (1%2F5,-1%2F2), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=%28-1%2F2%29x-2%2F5 through the points (-7%2F5,3%2F10) and (1%2F5,-1%2F2)

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