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Answer: Choice B) $790</h3>
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Explanation:
x = number of months
y = account balance
The first column of the table has (x,y) = (8,470) to mean that on month 8, her balance was $470
Then we have (10, 390) meaning x = 10 and y = 39. As x increased by 2, y dropped by 470-390 = 80 dollars. She withdrew $80 over the course of two months. Therefore, she is withdrawing 80/2 = 40 dollars a month. This is the slope value. It represents the rate of change. We could use the slope formula to find the same result.
Let m = -40 be the slope. It's negative to indicate the value of y goes down as x goes up, or vice versa.
With m = -40, x = 8 and y = 470, we can find the y intercept b like so
y = mx+b
470 = -40*8+b
470 = -320+b
470+320 = b
790 = b
b = 790 is the y intercept, and it represents the initial account balance before Katie started withdrawing money.
In other words, it represents the starting amount of money she has.
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As a slight alternative, we could use the point slope form to find the y intercept
y - y1 = m(x - x1)
y - 470 = -40(x - 8)
y = -40(x-8) + 470
y = -40x + 320 + 470
y = -40x + 790
You don't have to use (x,y) = (8,470). You can use any column you want from the table of values. The value of m will be m = -40 the whole time however.
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As a way to check to see if we have the correct equation, try plugging in various values of x to see if you get the proper y values as outputs as shown in the table.
For instance, if we tried x = 10, then,
y = -40x + 790
y = -40*10 + 790
y = -400+790
y = 390
That confirms column 2. I'll let you verify the other columns.
