Question

Alex is trying to start a savings plan. The following graph represents his projected savings over the next 12 months. How many months will have passed until Alex has saved $800?

Question 19 options:



12 months



14 months



16 months



18 months

Answer 1

Answer: Choice B) 14 months

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Step-by-step explanation:

The two points (4,300) and (8,500) are on the line

Use the slope formula to get
m = (y2-y1)/(x2-x1)
m = (500-300)/(8-4)
m = 200/4
m = 50
The slope is 50

Use the slope of m = 50 along with one of the points, say (x,y) = (4,300)
Plug them into the y = mx+b formula. Then solve for b

y = mx+b
300 = 50*4+b
300 = 200+b
300-200 = 200+b-200
100 = b
b = 100
The y intercept is 100
This is the location where the blue graph crosses the y axis

Since m = 50 is the slope and b = 100 is the y intercept, this means y = 50x+100 is the equation that generates that line

After we get the equation, we replace y with 800 and solve for x. The reason why is because we want to know the x value (the number of months) when the y value is 800 (when money saved is $800)

So,
y = 50x+100
800 = 50x+100
800-100 = 50x+100-100
700 = 50x
50x = 700
50x/50 = 700/50
x = 14
So it takes 14 months

Answer 2

From the graph, we can tell that every 4 months, $200 is saved. If at 12 months, he has saved $700, we know that it will take another 2 months to save another $100. Therefore, 14 months is your answer