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)

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) (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) (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 (,) and (,)

Start with the slope formula (note: (,) is the first point (,) and (,) is the second point (,))

Plug in ,,, (these are the coordinates of given points)

Subtract the terms in the numerator to get . Subtract the terms in the denominator to get

So the slope is

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

Now let's use the point-slope formula to find the equation of the line:

------Point-Slope Formula------
where is the slope, and (,) is one of the given points

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get . Now reduce to get

Add to both sides to isolate y

Combine like terms and to get

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

Answer:

So the equation of the line which goes through the points (,) and (,) is:

The equation is now in form (which is slope-intercept form) where the slope is and the y-intercept is

Notice if we graph the equation and plot the points (,) and (,), we get this: (note: if you need help with graphing, check out this solver )

Graph of through the points (,) and (,)

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

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

Plug in x=1

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:

and $8 per hour + $12 translates to:

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

Subtract 8x from both sides

Divide both sides by 12

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

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