Answer:
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.
