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? on the graph there is points at (-5, -1) and (5, 7)

Answer 1

To find the rate of change of \( y \) with respect to \( x \) for the line passing through the points \((-5, -1)\) and \((5, 7)\), we can use the formula for the slope \( m \):

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

Here, \((x_1, y_1) = (-5, -1)\) and \((x_2, y_2) = (5, 7)\). Plugging in these values:

\[ m = \frac{7 - (-1)}{5 - (-5)} \]

This simplifies to:

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

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

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