Answer:
[tex]\Huge\boxed{\$ 12.12}[/tex]
Step-by-step explanation:
In order to find how much credit is left after 92 minutes, we need to
1. Figure out the equation that describes this graph (since we don't know the y-intercept)
2. Find the credit remaining after 92 minutes using the equation formed.
Figuring out the equation of this graph:
First things first is to figure out the slope of this graph. Since this is a linear function, the slope will remain constant, and we can note something about slope here.
The slope of a line will be it's change in x divided by its change in y, often referred to with a formula.
[tex]\frac{\Delta y}{\Delta x}[/tex]
Since we know two points on this graph, we can find the changes in the x and y then divide for the slope.
Since minutes used is the x, and credit left is the y, we have two points.
(41, 19.26) and (68, 15.48).
- The change in y is -3.78, as [tex]19.26-15.48=3.87[/tex], and we decreased, so -3.78.
- The change in x is 27 as [tex]68-41=27[/tex], and we increased.
The slope will then be [tex]\frac{-3.78}{27}[/tex] which comes out to be -0.14.
Now that we know the slope, that means our equation will look something like [tex]y = -0.14x+b[/tex] - however, we still have b to solve for!
To solve for it, we can substitute one of our points in - let's do (41, 19.26) - to the equation and solve for b.
- [tex]19.26 =-0.14 \cdot 41 +b[/tex]
- [tex]19.26 = -5.74+ b[/tex]
- [tex]b = 19.26+5.74[/tex]
- [tex]b = 25[/tex]
Now that we know that b = 25, we can plug it into our equation, making the final equation that represents this scenario
[tex]y = -0.14x+25[/tex]
Solving for 92 minutes
Now that we know the equation to our graph, we can substitute in 92 minutes as the x value to find our y value (credit left).
- [tex]y = -0.14 \cdot 92 + 25[/tex]
- [tex]y = -12.88+25[/tex]
- [tex]y =12.12[/tex]
Therefore, after 92 minutes, the amount of credit left is $12.12
Hope this helped!
