Question

A linear function includes the points (2, 3) and (6, 8). What is the rate of change of the linear function, and can someone help, please?

Please note that the rate of change in this context is often referred to as the slope of the linear function, which you can find by calculating the difference in the y-coordinates divided by the difference in the x-coordinates of the two given points.

Answer 1

The rate of change (slope) of the linear function that includes the points (2, 3) and (6, 8) is calculated using the slope formula m = (y2 - y1) / (x2 - x1). The slope is found to be 5/4 or 1.25, meaning there is a rise of 1.25 on the y-axis for every 1 unit increase on the x-axis.

Step-by-step explanation:

The rate of change of a linear function represents how much the dependent variable (usually represented as y) changes for each unit of change in the independent variable (x). This is often called the slope of the line. To calculate the slope, you need to follow these steps:

1. Choose two points on the line. For this example, we are given the points (2, 3) and (6, 8).
2. Use the formula for slope (m) which is m = (change in y) / (change in x). This is often written as m = (y2 - y1) / (x2 - x1).
3. Substitute the y and x values from your chosen points into the slope formula. Here, we get m = (8 - 3) / (6 - 2).
4. Calculate the numerator and denominator separately to find that the slope m = 5 / 4.

Therefore, the slope of the line, representing the rate of change, is 5/4 or 1.25. This means there is a rise of 1.25 units in y for every 1 unit increase in x.