SOLUTION: Which table will have the greatest value of y when x = 7? x 1 2 3 y 2 4 8 x 1 2 3 y 14 26 38 x 1 2 3 y 3 12 27 x 1 2 3 y 12 22 32

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons -> SOLUTION: Which table will have the greatest value of y when x = 7? x 1 2 3 y 2 4 8 x 1 2 3 y 14 26 38 x 1 2 3 y 3 12 27 x 1 2 3 y 12 22 32      Log On


   

Question 1027532: Which table will have the greatest value of y when x = 7?
x 1 2 3
y 2 4 8
x 1 2 3
y 14 26 38
x 1 2 3
y 3 12 27

x 1 2 3
y 12 22 32
Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
Which table will have the greatest value of y when x+=+7?
table 1:
x| +1++2++3}
y|++2++4++8
as you can see, equation for this table is y=2x
so, if x+=+7, then y+=highlight%28+14%29

table 2:
x| +1++2++3
y|++14++26++38
find formula first:
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,14) and (2,26)


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 (1,14) and (x%5B2%5D,y%5B2%5D) is the second point (2,26))


m=%2826-14%29%2F%282-1%29 Plug in y%5B2%5D=26,y%5B1%5D=14,x%5B2%5D=2,x%5B1%5D=1 (these are the coordinates of given points)


m=+12%2F1 Subtract the terms in the numerator 26-14 to get 12. Subtract the terms in the denominator 2-1 to get 1



So the slope is

m=12





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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-14=%2812%29%28x-1%29 Plug in m=12, x%5B1%5D=1, and y%5B1%5D=14 (these values are given)



y-14=12x%2B%2812%29%28-1%29 Distribute 12


y-14=12x-12 Multiply 12 and -1 to get -12%2F1. Now reduce -12%2F1 to get -12

y=12x-12%2B14 Add 14 to both sides to isolate y


y=12x%2B2 Combine like terms -12 and 14 to get 2

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Answer:



So the equation of the line which goes through the points (1,14) and (2,26) is:y=12x%2B2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=12 and the y-intercept is b=2


Notice if we graph the equation y=12x%2B2 and plot the points (1,14) and (2,26), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=12x%2B2 through the points (1,14) and (2,26)


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




equation for this table is y=12x%2B2
so, if x+=+7, than y+=+12%2A7%2B2=highlight%2886%29

table 3:
x| +1++2++3
y|+3++12++27
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,3) and (2,12)


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 (1,3) and (x%5B2%5D,y%5B2%5D) is the second point (2,12))


m=%2812-3%29%2F%282-1%29 Plug in y%5B2%5D=12,y%5B1%5D=3,x%5B2%5D=2,x%5B1%5D=1 (these are the coordinates of given points)


m=+9%2F1 Subtract the terms in the numerator 12-3 to get 9. Subtract the terms in the denominator 2-1 to get 1



So the slope is

m=9





------------------------------------------------


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-3=%289%29%28x-1%29 Plug in m=9, x%5B1%5D=1, and y%5B1%5D=3 (these values are given)



y-3=9x%2B%289%29%28-1%29 Distribute 9


y-3=9x-9 Multiply 9 and -1 to get -9%2F1. Now reduce -9%2F1 to get -9

y=9x-9%2B3 Add 3 to both sides to isolate y


y=9x-6 Combine like terms -9 and 3 to get -6

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Answer:



So the equation of the line which goes through the points (1,3) and (2,12) is:y=9x-6


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=9 and the y-intercept is b=-6


Notice if we graph the equation y=9x-6 and plot the points (1,3) and (2,12), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=9x-6 through the points (1,3) and (2,12)


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




equation for this table is: y=9x-6
so, if x+=+7, than y=9%2A7-6=highlight%2857%29

table 4:
x| +1++2++3
y|++12++22+32
find formula first:
Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,12) and (2,22)


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 (1,12) and (x%5B2%5D,y%5B2%5D) is the second point (2,22))


m=%2822-12%29%2F%282-1%29 Plug in y%5B2%5D=22,y%5B1%5D=12,x%5B2%5D=2,x%5B1%5D=1 (these are the coordinates of given points)


m=+10%2F1 Subtract the terms in the numerator 22-12 to get 10. Subtract the terms in the denominator 2-1 to get 1



So the slope is

m=10





------------------------------------------------


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-12=%2810%29%28x-1%29 Plug in m=10, x%5B1%5D=1, and y%5B1%5D=12 (these values are given)



y-12=10x%2B%2810%29%28-1%29 Distribute 10


y-12=10x-10 Multiply 10 and -1 to get -10%2F1. Now reduce -10%2F1 to get -10

y=10x-10%2B12 Add 12 to both sides to isolate y


y=10x%2B2 Combine like terms -10 and 12 to get 2

------------------------------------------------------------------------------------------------------------

Answer:



So the equation of the line which goes through the points (1,12) and (2,22) is:y=10x%2B2


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=10 and the y-intercept is b=2


Notice if we graph the equation y=10x%2B2 and plot the points (1,12) and (2,22), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=10x%2B2 through the points (1,12) and (2,22)


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




equation for this table is y=10%2B2
so, if x+=+7, than y+=+10%2A7%2B2=highlight%2872%29


answer: table 2 will have the greatest value of y when x+=+7