Question
Jakob draws the graph of a linear function. If the graph includes the points (−4,−2)
and (0,0)
, what is the rate of change of Jakob’s function expressed as a decimal?(1 point)
The rate of change of Jakob’s function is
.
and (0,0)
, what is the rate of change of Jakob’s function expressed as a decimal?(1 point)
The rate of change of Jakob’s function is
.
Answers
GPT-4o mini
To find the rate of change (slope) of the linear function defined by the points \((-4, -2)\) and \((0, 0)\), we can use the slope formula:
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Assigning the points where \((x_1, y_1) = (-4, -2)\) and \((x_2, y_2) = (0, 0)\), we can substitute into the formula:
\[
m = \frac{0 - (-2)}{0 - (-4)} = \frac{0 + 2}{0 + 4} = \frac{2}{4} = \frac{1}{2}
\]
Expressed as a decimal, the rate of change is:
\[
0.5
\]
Thus, the rate of change of Jakob's function is \(0.5\).
\[
m = \frac{y_2 - y_1}{x_2 - x_1}
\]
Assigning the points where \((x_1, y_1) = (-4, -2)\) and \((x_2, y_2) = (0, 0)\), we can substitute into the formula:
\[
m = \frac{0 - (-2)}{0 - (-4)} = \frac{0 + 2}{0 + 4} = \frac{2}{4} = \frac{1}{2}
\]
Expressed as a decimal, the rate of change is:
\[
0.5
\]
Thus, the rate of change of Jakob's function is \(0.5\).