Eric received a gift card worth $25 as a birthday present. He is spending $2.50 per day using the gift card, as shown in the graph below. Which statement is true about the linear function that represents his gift card spending?
A graph titled Eric's Gift Card Spending has time (days) on the x-axis and Amount left on card (dollars) on the y-axis. A line goes through points (2, 20), (3, 17.5), (4, 15).
The initial value is the amount on the gift card before Eric starts using it.
The initial value is the amount on the gift card after Eric finishes using it.
The rate of change is the amount on the gift card before Eric starts using it.
The rate of change is the amount on the gift card after Eric finishes using it.
The initial value is the amount on the gift card before Eric starts using it.
To determine the true statement about the linear function that represents Eric's gift card spending, we need to analyze the graph provided.
The graph shows that Eric spends $2.50 each day using the gift card. Given this information, we can determine the equation of the linear function that represents his spending.
Using the point-slope form of a linear equation (y - y1 = m(x - x1)), let's calculate the slope, m, which represents the rate of change.
Taking two points (2, 20) and (3, 17.5) from the graph, we can calculate the slope:
m = (17.5 - 20) / (3 - 2)
m = -2.5
Thus, the slope (rate of change) is -2.5, indicating that the amount on the gift card decreases by $2.50 each day.
Now, let's determine the initial value, which is the amount on the gift card before Eric starts using it. We can do this by substituting the coordinates of a given point (2, 20) into the linear equation.
Using the point-slope form, we have:
y - y1 = m(x - x1)
y - 20 = -2.5(x - 2)
y - 20 = -2.5x + 5
y = -2.5x + 25
The equation of the linear function representing Eric's gift card spending is y = -2.5x + 25.
By analyzing the equation, we can determine that the initial value represents the amount on the gift card before Eric starts using it. Therefore, the correct statement is: The initial value is the amount on the gift card before Eric starts using it.
The statement that is true about the linear function that represents Eric's gift card spending is:
The rate of change is the amount on the gift card after Eric finishes using it.