Answer :
Answer:
A The information in the table has a constant rate of change of 3.5.
Step-by-step explanation:
A linear equation is in the form y = mx + b, where y is a dependent variable, x is an independent variable, m is the rate of change (slope) and b is the value of y when x = 0.
Let y represent the cost of a corsage and x represent the number of flowers in the corsage
The table (x, y) has the points (2, 7) and (3, 10.5). The equation is given by:
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)\\\\y-7=\frac{10.5-7}{3-2}(x-2)\\\\y-7=3.5(x-2)\\\\y-7=3.5x-7\\\\y=3.5x[/tex]
Therefore the rate of change is 3.5
The data in the given table has a constant rate of change of $3.50 for each additional flower in the corsage, which aligns with option A.
The relationship between the cost of a corsage and the number of flowers is illustrated by the given data. To determine the constant rate of change, we can calculate the difference in cost with respect to the number of flowers. We'll look at the increments:
- From 2 to 3 flowers, the cost increases from $7.00 to $10.50, which is a $3.50 increase.
- From 3 to 4 flowers, the cost increases from $10.50 to $14.00, which is also a $3.50 increase.
- From 4 to 5 flowers, the cost increases from $14.00 to $17.50, which is again a $3.50 increase.
This indicates that for each additional flower, the cost increases by $3.50. Therefore, the correct statement about the information in the table is that the data has a constant rate of change of 3.5, meaning option A is true.
