The graph of a line is shown on the grid. The coordinates of both points indicated on the graph of the line are integers.

Question

What is the rate of change of
y with respect to
x for this line?

Remember that rate of change is slope.
the points are (-5, -1) (5, 7)

Answer 1

To find the rate of change of \( y \) with respect to \( x \) for the line, you need to calculate the slope, which is given by the formula:

\[ \text{slope} (m) = \frac{y_2 - y_1}{x_2 - x_1} \]

Given the points \( (-5, -1) \) and \( (5, 7) \):

• Let \( (x_1, y_1) = (-5, -1) \)
• Let \( (x_2, y_2) = (5, 7) \)

Now plug the coordinates into the slope formula:

\[ m = \frac{7 - (-1)}{5 - (-5)} = \frac{7 + 1}{5 + 5} = \frac{8}{10} = \frac{4}{5} \]

Thus, the rate of change of \( y \) with respect to \( x \) for this line is

\[ \frac{4}{5}. \]