Question
On a graph you have points (-1,-9) and (1,3) using interval [-1,1] what would be the rate of change
Answers
GPT-4o mini
To find the rate of change between two points on a graph, you can use the formula for the slope of the line connecting those points. The formula for the rate of change (slope) between two points \((x_1, y_1)\) and \((x_2, y_2)\) is:
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points \((-1, -9)\) and \((1, 3)\):
- \((x_1, y_1) = (-1, -9)\)
- \((x_2, y_2) = (1, 3)\)
Substituting the values into the formula:
\[
\text{slope} = \frac{3 - (-9)}{1 - (-1)} = \frac{3 + 9}{1 + 1} = \frac{12}{2} = 6
\]
Thus, the rate of change between the points \((-1, -9)\) and \((1, 3)\) is \(6\).
\[
\text{slope} = \frac{y_2 - y_1}{x_2 - x_1}
\]
Given the points \((-1, -9)\) and \((1, 3)\):
- \((x_1, y_1) = (-1, -9)\)
- \((x_2, y_2) = (1, 3)\)
Substituting the values into the formula:
\[
\text{slope} = \frac{3 - (-9)}{1 - (-1)} = \frac{3 + 9}{1 + 1} = \frac{12}{2} = 6
\]
Thus, the rate of change between the points \((-1, -9)\) and \((1, 3)\) is \(6\).