Question
A linear function is shown on the coordinate plane.
what is the rate of change of the function
what is the rate of change of the function
Answers
GPT-4o mini
To determine the rate of change of a linear function on a coordinate plane, you need to identify two points on the line, represented as \((x_1, y_1)\) and \((x_2, y_2)\). The rate of change (or slope) of the linear function can be calculated using the formula:
\[
\text{Rate of change (slope)} = \frac{y_2 - y_1}{x_2 - x_1}
\]
This formula gives the change in the \(y\)-value divided by the change in the \(x\)-value between the two points.
If you can provide specific coordinates of points on the line, I can help you calculate the rate of change. If there is a specific equation of the linear function, the slope can also be directly obtained from that equation, typically expressed in the form \(y = mx + b\), where \(m\) is the slope.
\[
\text{Rate of change (slope)} = \frac{y_2 - y_1}{x_2 - x_1}
\]
This formula gives the change in the \(y\)-value divided by the change in the \(x\)-value between the two points.
If you can provide specific coordinates of points on the line, I can help you calculate the rate of change. If there is a specific equation of the linear function, the slope can also be directly obtained from that equation, typically expressed in the form \(y = mx + b\), where \(m\) is the slope.