Question

What's the slope for cost and square footage of carpet?
(10,25) (20,30) (30,45) (40,60) (50,75)

Answer 1

To find the slope of the line that represents the relationship between cost and square footage of carpet, we can use any two points from the given set of coordinates. The formula for calculating the slope \( m \) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:

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

Let's use the first two points: \((10, 25)\) and \((20, 30)\).

Here,

- \(x_1 = 10\), \(y_1 = 25\)
- \(x_2 = 20\), \(y_2 = 30\)

Now, substituting these values into the slope formula:

\[
m = \frac{30 - 25}{20 - 10} = \frac{5}{10} = \frac{1}{2}
\]

Thus, the slope of the line representing the cost and square footage of carpet is \( \frac{1}{2} \).

You can check that this slope remains consistent with other pairs of points. For instance, using the points \((20, 30)\) and \((30, 45)\):

\[
m = \frac{45 - 30}{30 - 20} = \frac{15}{10} = \frac{3}{2}
\]

However, this shows a different slope; confirming that as square footage increases the cost does not increase at a constant rate.

Choosing pairs accordingly may yield different slopes, thus indicating that the changes in cost relative to changes in square footage aren't constant across the provided points.

To accurately represent all data, consider fitting a line or a different function if you require a better model.