Answer:
C. The point (20, 45) is on the line.
Step-by-step explanation:
The number of songs learned by Audra vs the number of months is plotted in the graph provided.
Some points are recognized from the graph: (0,5) (1,7) (2,9) among others. With two of these points, we construct the linear model of the graph.
The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:
[tex]\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)[/tex]
Using (0,5) and (1,7):
[tex]\displaystyle y-5=\frac{7-5}{1-0}(x-0)[/tex]
[tex]\displaystyle y-5=\frac{2}{1}(x-0)[/tex]
y - 5 = 2x
y = 2x + 5
The slope of the line is 2. So, A. and B are discarded.
The y-intercept represents the number of songs Audra played initially at time = 0.
The point (20,45) is on the line as we'll prove below:
y = 2(20) + 5 = 40 + 5 = 45
When x=20, y=45
Thus, the correct choice is:
C. The point (20, 45) is on the line.
