Solution:
Given the table showing the relationship between x and y, below:
We can represent the relationship between x and y using the equation of a line expressed as
step 1: Evaluate the slope m of the line.
The slope m of the line is expressed as
To find the equation of the line, we select two points (x, y) from the table of values.
Thus, selecting the points (-1,-1) and (0,1), this implies that
Substituting these values into equation 2, we have
step 2: Evaluate the y-intercept of the line.
The y-intercept of the line is the value of y when the line cuts the y-axis. In other words, it's the value of y when the value of x equals zero.
In the table of values, when the value of x equals zero, the value of y is 1.
Thus, the y-intercept of the line is
step 3: Substitute the values of m and c into equation 1.
From equation 1,
Thus, the function that represents the relationship between the quantities in the table is
The correct option is F.