Answer:
The rate of change of the weight of kitten A is greater than the rate of change of the weight of kitten B
Step-by-step explanation:
- The rate of change of the linear relationship is the slope of the line which represent this relationship
- The rule of the slope is m = [tex]\frac{y2-y1}{x2-x1}[/tex] , where (x1, y1) and (x2, y2) are 2 points on the line
∵ The table shows the weight gain of kitten A
→ Choose two points from the table to find the slope
∵ Points (0, 3) and (1, 7) are two points in the table
∴ x1 = 0 and y1 = 3
∴ x2 = 1 and y2 = 7
→ Substitute them in the rule of the slope above
∵ m = [tex]\frac{7-3}{1-0}[/tex] = [tex]\frac{4}{1}[/tex] = 4
∵ The slope is the rate of change
∴ The rate of change of the weight of kitten A is 4 oz/week
∵ The graph shows the weight gain of kitten B
→ Choose two points on the line to find the slope
∵ Points (0, 4) and (2, 10) lies on the line
∴ x1 = 0 and y1 = 4
∴ x2 = 2 and y2 = 10
→ Substitute them in the rule of the slope above
∵ m = [tex]\frac{10-4}{2-0}[/tex] = [tex]\frac{6}{2}[/tex] = 3
∵ The slope is the rate of change
∴ The rate of change of the weight of kitten B is 3 oz/week
→ By comparing the two rates
∵ The rate of change of kitten A is 4 oz per week
∵ The rate of change of kitten B is 3 oz per week
∴ The rate of change of the weight of kitten A is greater than
the rate of change of the weight of kitten B
