SOLUTION: This is the first time I need help bad and using this. I have to write an equation that models between time and distance using this chart. on the chart (time[seconds]=distance)

Algebra ->  Equations -> SOLUTION: This is the first time I need help bad and using this. I have to write an equation that models between time and distance using this chart. on the chart (time[seconds]=distance)      Log On


   

Question 82170: This is the first time I need help bad and using this. I have to write an equation that models between time and distance using this chart.
on the chart (time[seconds]=distance) 1=1100 2=2200 3=3300 4=4400 5=5500



Also, i need help with this problem.
What number of hours are the two plans equal?
Plan A; $20 per hour
Plan B: $8 per hour + $12
If you can help me thank you very much!
Found 2 solutions by lovebug93, jim_thompson5910:
Answer by lovebug93(2) About Me  (Show Source):
You can put this solution on YOUR website!
all u do is times 1100 by x for #1
and for #2 u just times 20 by w/e to match up wit the other equation

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
Let x=time, y=distance
Since we have a relationship between the time and distances, we can say that these times and distances follow a pattern. We can find the formula for this pattern by letting x=1 second and y=1100 to get one point (1,1100). Now let x=2 and y=2200. Now that we have 2 points (1,1100) and (2,2200) and we can now make a line

Solved by pluggable solver: Finding the Equation of a Line
First lets find the slope through the points (1,1100) and (2,2200)


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 (1,1100) and (x%5B2%5D,y%5B2%5D) is the second point (2,2200))


m=%282200-1100%29%2F%282-1%29 Plug in y%5B2%5D=2200,y%5B1%5D=1100,x%5B2%5D=2,x%5B1%5D=1 (these are the coordinates of given points)


m=+1100%2F1 Subtract the terms in the numerator 2200-1100 to get 1100. Subtract the terms in the denominator 2-1 to get 1



So the slope is

m=1100





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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-1100=%281100%29%28x-1%29 Plug in m=1100, x%5B1%5D=1, and y%5B1%5D=1100 (these values are given)



y-1100=1100x%2B%281100%29%28-1%29 Distribute 1100


y-1100=1100x-1100 Multiply 1100 and -1 to get -1100%2F1. Now reduce -1100%2F1 to get -1100

y=1100x-1100%2B1100 Add 1100 to both sides to isolate y


y=1100x%2B0 Combine like terms -1100 and 1100 to get 0

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Answer:



So the equation of the line which goes through the points (1,1100) and (2,2200) is:y=1100x%2B0


The equation is now in y=mx%2Bb form (which is slope-intercept form) where the slope is m=1100 and the y-intercept is b=0


Notice if we graph the equation y=1100x%2B0 and plot the points (1,1100) and (2,2200), we get this: (note: if you need help with graphing, check out this solver)


Graph of y=1100x%2B0 through the points (1,1100) and (2,2200)


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





So we can see that equation is y=1100x. We can check this by plugging in x=1 to get

y=1100%281%29 Plug in x=1

y=1100 works
And we can do this for every x to verify.



For the second problem, we're going to make equations of the two plans and find out where they intersect:
So $20 an hour translates to this equation:
y=20x

and $8 per hour + $12 translates to:

y=8x%2B12

So now set them equal to each other to see when the plans will be the same

20x=8x%2B12

20x-8x=cross%288x-8x%29%2B12 Subtract 8x from both sides

12x=12

cross%2812%2F12%29x=12%2F12 Divide both sides by 12

x=1

So the plans are equal at x=1, which is 1 hour.