Question
If a linear function has the points (2,3) and (negative 5,negative 1) on its graph, what is the rate of change of the function?
Answers
GPT-4o mini
To find the rate of change of a linear function given two points, you can use the formula for the slope (rate of change) \(m\):
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (-5, -1)\).
Plugging in the coordinates, we have:
\[
m = \frac{-1 - 3}{-5 - 2}
\]
Now, calculate the numerator and denominator:
Numerator:
\(-1 - 3 = -4\)
Denominator:
\(-5 - 2 = -7\)
Now, substitute these values back into the slope formula:
\[
m = \frac{-4}{-7} = \frac{4}{7}
\]
Therefore, the rate of change of the function is \(\frac{4}{7}\).
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
where \((x_1, y_1) = (2, 3)\) and \((x_2, y_2) = (-5, -1)\).
Plugging in the coordinates, we have:
\[
m = \frac{-1 - 3}{-5 - 2}
\]
Now, calculate the numerator and denominator:
Numerator:
\(-1 - 3 = -4\)
Denominator:
\(-5 - 2 = -7\)
Now, substitute these values back into the slope formula:
\[
m = \frac{-4}{-7} = \frac{4}{7}
\]
Therefore, the rate of change of the function is \(\frac{4}{7}\).