First, use the given points to calculate the slope.
Then, identify the y-intercept.
B
Recall the meaning of x and y.
A
y=0.5x+11
B
See solution.
Practice makes perfect
We are given a table that shows the length y in inches of a person's hair after x months.
Months, x
Hair Length, y
0
11.0
3
12.5
6
14.0
Functions written in slope-intercept form follow a specific format.
y= mx+ b
In this form, m is the slope and b is the y-intercept. We need to identify these values using the given table. Let's start by substituting the points (0,11) and (3,12.5), into the slope formula and calculating m.
We calculated that the slope of the given equation is 0.5, which means that each month the hair increases by 0.5 inches. Now, remember that the y-intercept is the y-value where the line crosses the y-axis. It occurs when x=0. From the table we can see that when x=0, the value of y= 11.
Months, x
Hair Length, y
0
11.0
3
12.5
6
14.0
The function intercepts the y-axis at (0, 11), which means that there are 11 inches of hair in the beginning. Therefore, the value of b is 11. Now that we have the slope and the y-intercept, we can write a function for the line that passes through the given points.
y= 0.5x+ 11
Recall the function obtained in Part A.
y= 0.5x+ 11
Here, y represents the hair length in inches and x the amount of months. The slope of the function represents that the amount of new hair each month and the y-intercept represents the amount of hair at the beginning. Therefore, the hair length at the beginning was 11 inches and it grows 0.5 each month.
