The distance y (in miles) that Train A travels in x hours is represented by the equation y=68x . The graph shows the distance that Train B travels. (0, 0) and (1, 64).

Answer:

For train A, the distance traveled as a function of time in hours is written as:

y = 68*x

For train B, we know that it's equation passes through the points (0, 0) and (1, 64)

Remember that:

A linear relationship can be written as:

y = a*x + b

where a is the slope and b is the y-axis intercept.

For a line that passes through the points (x1, y1) and (x2, y2), the slope can be written as:

a = (y2 - y1)/(x2 - x1).

Then the slope for the equation of train B is:

a = (64 - 0)/(1 - 0) = 64

Then equation of train B is something like:

y = 64*x + b

Now, we know that it passes through the point (0, 0), this means that when x = 0, we also have y = 0, then if we replace these two values in the equation we get:

0 = 64*0 + b

0 = 0 +b

then b = 0

This means that the equation for train B is:

y = 64*x

Where again, y is the distance in miles and x is the time in hours.

If we look at both equations, we can see that train A has a larger slope, which means that for each unit of time, train A travels a larger distance, then we can conclude that train A is faster than train B.

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The Scenario:
The Powerball Lottery jackpot reaches 1.5 billion dollars, and Jeffrey decides to spend some money each week on lottery tickets. He puts some money in a new bank account and withdrawals the same amount once a week to try his luck at winning the jackpot. After three straight weeks of no luck, Jeffrey has $205 left in his account. After twelve total weeks, he still hasn’t won a thing and has $160 left to spend.
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a) Write an equation that models how much money is in Jeffrey’s account at any given week. Show all work in the space below. You can type your work, or insert a picture of hand-written work.
b) Write an equation that models how much money is in Karen’s account at any given week. Show all work in the space below. You can type your work, or insert a picture of hand-written work
c) Show algebraically when Jeffrey and Karen will have the same amount of money in their accounts. Show all steps.
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