Question

The graph of a linear function is shown on the grid. What is the rate of change of y
with respect to x
for this function?
choose one answer

(1 point)
Responses

7/9

3/4

−7/9

−3/4

Answer 1

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

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

You need two points from the graph of the linear function to calculate the slope. Once you identify these points, substitute their coordinates into the formula to calculate the slope.

Unfortunately, I don't have the visual of the graph you mentioned, but based on the given responses, you should follow these steps:

1. Pick two distinct points from the line (for example, point \( (x_1, y_1) \) and point \( (x_2, y_2) \)).
2. Calculate \( \Delta y = y_2 - y_1 \) and \( \Delta x = x_2 - x_1 \).
3. Calculate the slope using the values you obtained.

Once you do that, compare your result with the provided options: \( \frac{7}{9} \), \( \frac{3}{4} \), \( -\frac{7}{9} \), and \( -\frac{3}{4} \) to select the correct answer.

Please let me know if you have specific coordinates from the graph, and I can assist you in calculating the slope.