Jocelyn is saving money. She started with $0, and after 8 weeks, she had $60. Jocelyn is not sure exactly how much money she saved each week, but she assumes that she saved money at a constant rate from when she started saving money through Week 8.

We know that:

Jocelyn started with $0, this is represented with the point (0, $0)

After 8 weeks, she had $60, this is represented with the point (8, $60)

Jocelyn assumes that she saved money at a constant rate, so we can represent this with a linear relationship.

A linear relationship can be written as:

y = a*x + b

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

In our case, y is the amount of money that she has saved, x is the number of weeks since she started saving, the slope is the amount of money that she saves each week, and the y-intercept is the initial amount of money that she had saved.

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

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

In this case, our two points are:

(0, $0) and (8, $60), then the slope will be:

a = ($60 - $0)/(8 - 0) = $60/8 = $7.5

our equation is:

y = $7.5*x + b

To find the value of b, just replace both values in one of the points in the equation, for example, the point (0, $0)

$0 = $7.5*0 + b

$0 = b

Then our equation is:

y = $7.5*x     for 0 ≥ x ≥ 8

Where i added a restriction in the domain because this is described only for the first 8 weeks after she started saving money.

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step-by-step explanation:

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