SOLUTION: how would I graph the line with a slope of 3 and passes through points (2,1) and (4,7).

Algebra ->  Linear-equations -> SOLUTION: how would I graph the line with a slope of 3 and passes through points (2,1) and (4,7).      Log On


   

Question 115649: how would I graph the line with a slope of 3 and passes through points (2,1) and (4,7).
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
If you only want to graph the line, simply plot the two points (2,1) and (4,7) and draw a straight line through them.



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However, if you want to find the equation of the line, then...

First lets find the slope through the points (2,1) and (4,7)

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 (2,1) and is the second point (4,7))

m=%287-1%29%2F%284-2%29 Plug in y%5B2%5D=7,y%5B1%5D=1,x%5B2%5D=4,x%5B1%5D=2 (these are the coordinates of given points)

m=+6%2F2 Subtract the terms in the numerator 7-1 to get 6. Subtract the terms in the denominator 4-2 to get 2


m=3 Reduce

So the slope is
m=3

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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-1=%283%29%28x-2%29 Plug in m=3, x%5B1%5D=2, and y%5B1%5D=1 (these values are given)


y-1=3x%2B%283%29%28-2%29 Distribute 3

y-1=3x-6 Multiply 3 and -2 to get -6

y=3x-6%2B1 Add 1 to both sides to isolate y

y=3x-5 Combine like terms -6 and 1 to get -5
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Answer:


So the equation of the line which goes through the points (2,1) and (4,7) is:y=3x-5

The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=3 and the y-intercept is b=-5

Notice if we graph the equation y=3x-5 and plot the points (2,1) and (4,7), we get this: (note: if you need help with graphing, check out this solver)

Graph of y=3x-5 through the points (2,1) and (4,7)

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