Question

Jakob draws the graph of a linear function. If the graph includes the points (-4,-2) and (0,0), what is the rate of change of Jakob's function expressed as a decimal?

Answer 1

To find the rate of change of the linear function represented by the points (-4, -2) and (0, 0), we can calculate the slope of the line defined by these two points.

The formula for the slope (rate of change) \( m \) between two points \( (x_1, y_1) \) and \( (x_2, y_2) \) is given by:

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

For the points (-4, -2) and (0, 0), we can assign the coordinates as follows:
- \( (x_1, y_1) = (-4, -2) \)
- \( (x_2, y_2) = (0, 0) \)

Substituting these values into the slope formula, we have:

\[
m = \frac{0 - (-2)}{0 - (-4)} = \frac{0 + 2}{0 + 4} = \frac{2}{4} = \frac{1}{2}
\]

Now, we convert the fraction \( \frac{1}{2} \) into a decimal:

\[
\frac{1}{2} = 0.5
\]

Therefore, the rate of change of Jakob's function expressed as a decimal is:

\[
\boxed{0.5}
\]