EXPLANATION
Let's see the facts:
Graph------> relationship between Hours that Narita works: y versus total amount of money she earns: x
A. The point (4,36) represents that she earns $36 dollars by working 4 hours.
B. The point (0,0) is the origin and represents that she don't earns money if she doesn't work.----> y-inter
C. In order to calculate how much she earns for each hour she works we need to obtain the slope as show as follows:
[tex]\text{Slope = }\frac{(y_2-y_1)}{(x_2-x_1)}[/tex]We can use any pair to obtain the slope, for instance let's take the pairs (x1,y1)=(0,0) and (x2,y2)=(4,36), so the slope will be:
[tex]\text{Slope}=\frac{(36-0)}{(4-0)}=\frac{36}{4}=9[/tex]Now, we can see that 9 represents the unit rate or the amount that she earns for each hour, so:
C. is $9/hour
D.
As we can see, this is a linear function, so the equation will be:
y=mt + b ----> m is the slope, t is the number of hours worked and b is the y-intercept
Replacing m=9:
y=9t + b
As we can see in the graph, the y-intercept is in x=0, so b=0
y=9t
------->D. The equation that could be used to find the total amount of money that Narita earns is y=9t.
