SOLUTION: Write an equation of the line that passes through points 1,5 and 2,3 My work: M=-2 (was hard to show how I got the answer so I'm just gonna put what I got) Y=MX+b 5=-2+b 5-2=b

Algebra ->  Linear-equations -> SOLUTION: Write an equation of the line that passes through points 1,5 and 2,3 My work: M=-2 (was hard to show how I got the answer so I'm just gonna put what I got) Y=MX+b 5=-2+b 5-2=b      Log On


   

Question 1019381: Write an equation of the line that passes through points 1,5 and 2,3
My work:
M=-2 (was hard to show how I got the answer so I'm just gonna put what I got)
Y=MX+b
5=-2+b
5-2=b
3=b
M=-2
B=3
Y=-2x+3
The teacher told me that the correct answer was y=-2x+7
How did she get that?
Answer by MathLover1(20849) 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 (1,5) and (2,3)


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 (1,5) and (x%5B2%5D,y%5B2%5D) is the second point (2,3))


m=%283-5%29%2F%282-1%29 Plug in y%5B2%5D=3,y%5B1%5D=5,x%5B2%5D=2,x%5B1%5D=1 (these are the coordinates of given points)


m=+-2%2F1 Subtract the terms in the numerator 3-5 to get -2. Subtract the terms in the denominator 2-1 to get 1



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



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


y-5=-2x%2B2 Multiply -2 and -1 to get 2%2F1. Now reduce 2%2F1 to get 2

y=-2x%2B2%2B5 Add 5 to both sides to isolate y


y=-2x%2B7 Combine like terms 2 and 5 to get 7

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Answer:



So the equation of the line which goes through the points (1,5) and (2,3) is:y=-2x%2B7


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=7


Notice if we graph the equation y=-2x%2B7 and plot the points (1,5) and (2,3), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=-2x%2B7 through the points (1,5) and (2,3)


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