SOLUTION: Given a line containing the points (1,4),(2,7),and(3,10) determine the slope-intercept form of the equation, provide one additional point on this line, and graph the function.

Algebra ->  Linear-equations -> SOLUTION: Given a line containing the points (1,4),(2,7),and(3,10) determine the slope-intercept form of the equation, provide one additional point on this line, and graph the function.      Log On


   

Question 87297: Given a line containing the points (1,4),(2,7),and(3,10) determine the slope-intercept form of the equation, provide one additional point on this line, and graph the function.
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Lets find the equation of the line through the two points (1,4) and (3,10)

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,4) and (3,10)


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 (1,4) and (x%5B2%5D,y%5B2%5D) is the second point (3,10))


m=%2810-4%29%2F%283-1%29 Plug in y%5B2%5D=10,y%5B1%5D=4,x%5B2%5D=3,x%5B1%5D=1 (these are the coordinates of given points)


m=+6%2F2 Subtract the terms in the numerator 10-4 to get 6. Subtract the terms in the denominator 3-1 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 (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-4=%283%29%28x-1%29 Plug in m=3, x%5B1%5D=1, and y%5B1%5D=4 (these values are given)



y-4=3x%2B%283%29%28-1%29 Distribute 3


y-4=3x-3 Multiply 3 and -1 to get -3%2F1. Now reduce -3%2F1 to get -3

y=3x-3%2B4 Add 4 to both sides to isolate y


y=3x%2B1 Combine like terms -3 and 4 to get 1

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Answer:



So the equation of the line which goes through the points (1,4) and (3,10) is:y=3x%2B1


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=1


Notice if we graph the equation y=3x%2B1 and plot the points (1,4) and (3,10), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=3x%2B1 through the points (1,4) and (3,10)


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





Now lets plot the point (2,7) and y=3x%2B1


graph of y=3x%2B1 with the point (2,7)

Since the point is on the line, the equation of the line that goes through (1,4),(2,7),and(3,10) is y=3x%2B1

Now lets pick any other x value so we can plot another point. Let x=0

3%280%29%2B1=0%2B1=1 plug in x=0

So we have another point (0,1)

So we have this graph and these points

graph of y=3x%2B1 with the points (0,1),(1,4),(2,7), and (3,10)