4. Suppose that you after 3 months you have \$350 in yor account and after 7 months you have \$650.

• a) Let x denote the number of months the and let y denote the amount of money in the account. Find a linear equation which will predict how much money you will have in the account as a function of the number of months
• b) Graph this function.
• c) Use this function to determine how much money you will have after 12 months.

a) If we let   x   denote the number of months the and let   y   denote the amount of money in the account, then

x1 = 3, y1 = 350

and

x2 = 7, y2 = 650

To find a linear equation, first find the slope.

= \$75/mo

Next, use the point-slope form of the equation

y - y1 = m(x - x1 )

Plug in our numbers.

y - 350 = 75(x - 3)

To solve for   y,   remove parentheses,

y - 350 = 75x - 225

and add 350 to both sides

y = 75x - 225 + 350

y = 75x + 125

This would tell you how much money you would have in your account if you opened the account with \$125 and put in \$75 each month (and there was no interest accumulating).

b) The graph would look like

c) To compute the amount after 12 months, we plug in a 12 for the   x   in the equation.

y = 75(12) + 125

= 900 + 125

= 1025

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