SOLUTION: can you check my work to make sure it is correct: find an equation for the line. write the equation in standard form through (3,-7) and (-1,10). M=(10) – (-7) (-1)-

Algebra ->  Linear-equations -> SOLUTION: can you check my work to make sure it is correct: find an equation for the line. write the equation in standard form through (3,-7) and (-1,10). M=(10) – (-7) (-1)-       Log On


   

Question 1048564: can you check my work to make sure it is correct:
find an equation for the line. write the equation in standard form
through (3,-7) and (-1,10).
M=(10) – (-7)
(-1)- (3)
M=-17
4
y-y1 = m(x-x1)
y-(-7)=-17 (x-3)
4
4y-(-7)=4-17 (x+3)
4
4y-=-17x+4y=23
4y-8=-17(x+3)
4y-8=-17(x-3)
+8_____+8
4x=17x-4y ANSWER
Answer by MathLover1(20850) 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,-7) and (-1,10)


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,-7) and (x%5B2%5D,y%5B2%5D) is the second point (-1,10))


m=%2810--7%29%2F%28-1-3%29 Plug in y%5B2%5D=10,y%5B1%5D=-7,x%5B2%5D=-1,x%5B1%5D=3 (these are the coordinates of given points)


m=+17%2F-4 Subtract the terms in the numerator 10--7 to get 17. Subtract the terms in the denominator -1-3 to get -4




m=-17%2F4 Reduce



So the slope is

m=-17%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--7=%28-17%2F4%29%28x-3%29 Plug in m=-17%2F4, x%5B1%5D=3, and y%5B1%5D=-7 (these values are given)



y%2B7=%28-17%2F4%29%28x-3%29 Rewrite y--7 as y%2B7



y%2B7=%28-17%2F4%29x%2B%28-17%2F4%29%28-3%29 Distribute -17%2F4


y%2B7=%28-17%2F4%29x%2B51%2F4 Multiply -17%2F4 and -3 to get 51%2F4

y=%28-17%2F4%29x%2B51%2F4-7 Subtract 7 from both sides to isolate y


y=%28-17%2F4%29x%2B23%2F4 Combine like terms 51%2F4 and -7 to get 23%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 (3,-7) and (-1,10) is:y=%28-17%2F4%29x%2B23%2F4


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=-17%2F4 and the y-intercept is b=23%2F4


Notice if we graph the equation y=%28-17%2F4%29x%2B23%2F4 and plot the points (3,-7) and (-1,10), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=%28-17%2F4%29x%2B23%2F4 through the points (3,-7) and (-1,10)


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