We want to determine if our friend's hair grows faster than the average hair growth. We are given a table that shows our friend's hair growth.
Months
1
2
3
4
Hair Growth (centimeters)
1.5
3
4.5
6
We can use the information in the table to graph our friend's hair growth y after x months. Every ordered pair created by the data in the table represents a point on this graph.
( months, centimeters)
( 1, 1.5),( 2, 3),( 3, 4.5),( 4, 6)
We can draw a line through the points (1,1.5), (2,3), (3,4.5), and (4,6) to get our graph. Let's do it!
Next, we can use the graph to calculate the slope. We calculate the change in y and the change in x between our points.
Now, we can calculate the slope.
slope=change iny/change inx=1.5/1= 1.5
This means that our friend's hair grows 1.5 centimeters per month. Let's compare this rate with the average hair growth of 15 centimeters per year. One year is 12 months. Therefore, we will divide 15 by 12 to get the average per month.
Finally, we compare our friend's hair growth of 1.5 centimeters per month with the average hair growth of 1.25 centimeters per month. We see that 1.5 is greater than 1.25.
1.5 > 1.25
Our friend's hair grows faster than the average hair growth.
We want to graph the average hair growth and the hair growth of our friend in the same coordinate plane. We know that hair growth is a proportional relationship with the number of months. This means that both equations will fit the general form, where m represents the slope of the graph.
y=mx
In Part A we found that our friend's hair grows 1.5 centimeters per month and that the average hair growth is 1.25 centimeters per month. We can substitute 1.5 and 1.25, one at a time, for m in the general equation to get our equations.
Our Friend's Hair Growth:& y=1.5x
Average Hair Growth:& y=1.25x
Now, we can plot the two equations in a coordinate plane.
We can see that the graph of our friend's hair growth is steeper than the graph of the average hair growth. This means that our friend's hair grows faster than the average hair growth.
