Prices from a T-Shirt shop are shown below. Find the rate of change for the situation.

Question

[You can use Slope Formula m, equals, start fraction, y, start subscript, 2, end subscript, minus, y, start subscript, 1, end subscript, divided by, x, start subscript, 2, end subscript, minus, x, start subscript, 1, end subscript, end fractionm=
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y
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OR add the table to Desmos and type y, start subscript, 1, end subscript, \sim, m, x, start subscript, 1, end subscript, plus, by
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∼mx
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+b to see mm ]

[Enter the number only]
Number of Shirts Total Price
13 148
18 203
21 236

Answer 1

To find the rate of change (slope) of the total price with respect to the number of shirts, we can use the slope formula:

\[ m = \frac{y_2 - y_1}{x_2 - x_1} \]

Where:

• \( (x_1, y_1) \) and \( (x_2, y_2) \) are two points on the line.

From the data:

• First point: \( (13, 148) \)
• Second point: \( (18, 203) \)

Now, we can compute the slope between these two points:

1. Let \( (x_1, y_1) = (13, 148) \) and \( (x_2, y_2) = (18, 203) \).
2. Plugging in the values:

\[ m = \frac{203 - 148}{18 - 13} = \frac{55}{5} = 11 \]

Next, let’s also calculate the slope between the second point and the third point:

• Second point: \( (18, 203) \)
• Third point: \( (21, 236) \)

Let \( (x_1, y_1) = (18, 203) \) and \( (x_2, y_2) = (21, 236) \).

\[ m = \frac{236 - 203}{21 - 18} = \frac{33}{3} = 11 \]

The rate of change (slope) between both pairs of points is the same, which is \( 11 \).

Thus, the rate of change is:

\[ \boxed{11} \]