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

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

Remember that rate of change is slope.

corridtes are 7,5 and -5,1

1 answer

To determine the rate of change (slope) of the line given the coordinates of two points, we use the slope formula:

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

Where:

  • \((x_1, y_1)\) and \((x_2, y_2)\) are the coordinates of the two points.

Given the points:

  • \((7, 5)\) (let's take this as \((x_1, y_1)\))
  • \((-5, 1)\) (let's take this as \((x_2, y_2)\))

Now we can substitute these values into the formula:

\[ m = \frac{1 - 5}{-5 - 7} \] \[ m = \frac{-4}{-12} \] \[ m = \frac{1}{3} \]

Thus, the rate of change (slope) of \(y\) with respect to \(x\) for this line is \(\frac{1}{3}\).