a) We can see that an increase in the number of employees (x) also leads to an increase in the number of products produced monthly, thus we can say that there is a positive correlation between the number of employees in the plant and the number of products produced monthly.
A positive correlation occurs when one variable increases with respect to another variable.
b) The function that best fits.
Let's first Find the rate of change(slope).
Take the points;
(x1, y1) ==> (0, 120)
(x2, y2) ==> (10, 200)
Use the slope formula:
[tex]m=\frac{y2-y1}{x2-x1}[/tex]
We have:
[tex]m=\frac{200-120}{10-0}=\frac{80}{10}=8[/tex]
Use the form:
y = mx + b
Where m is the slope and b is the y-intercept
We have:
y = 8x + b
Substitue 0 for x and 120 for y, to solve for b.
120 = 8(0) + b
120 = b
Thus, we have the function:
y = 8x + 120
f(x) = 8x + 120
c) The slope, m is = 8
The slope indicates that the avearge rate of change between both variables is 8.
The y-intercept can be said to be the point where the line of the plot crosses the y-axis. This means when the number of employees are is zero, the number of products will be 120.
It can also be called the constant value.
