Question

the graph of a linear function is shown on the grid.
a graph where the line goes from (-3, 3.6) to (5, 2)
what is the rate of change of y with respect to x for this function.

Answer 1

To find the rate of change of \( y \) with respect to \( x \) for a linear function, you can use the formula for the slope, which is given by:

\[
\text{slope} = \frac{\Delta y}{\Delta x} = \frac{y_2 - y_1}{x_2 - x_1}
\]

In this case, the points given are \((-3, 3.6)\) and \((5, 2)\). Let's denote these points as:
- \( (x_1, y_1) = (-3, 3.6) \)
- \( (x_2, y_2) = (5, 2) \)

Now, plug in these values into the slope formula:

\[
\Delta y = y_2 - y_1 = 2 - 3.6 = -1.6
\]
\[
\Delta x = x_2 - x_1 = 5 - (-3) = 5 + 3 = 8
\]

Now, calculate the slope:

\[
\text{slope} = \frac{-1.6}{8} = -0.2
\]

Thus, the rate of change of \( y \) with respect to \( x \) for this linear function is \(-0.2\).