Question

A linear function goes through two points (4, 4) and (2, 2), what is the slope?

Answer 1

The slope of the linear function is 1.

Step-by-step explanation:

A linear function is represented by the equation y = mx + b, where "m" is the slope. To find the slope, we can use the formula:

`\[ m = \frac{{\text{{change in }} y}}{{\text{{change in }} x}} \]`

Given two points (4, 4) and (2, 2), we can calculate the change in y and change in x as follows:

`\[ \Delta y = 4 - 2 = 2 \]`

`\[ \Delta x = 4 - 2 = 2 \]`

Now, substitute these values into the slope formula:

`\[ m = (2)/(2) = 1 \]`

The resulting slope is 1, indicating that for every unit increase in x, there is a corresponding unit increase in y. Therefore, the final answer is that the slope of the linear function passing through the points (4, 4) and (2, 2) is 1.

In summary, the slope is the ratio of the vertical change (change in y) to the horizontal change (change in x) between two points on the line. In this case, the slope of 1 signifies a consistent increase of 1 unit in y for every 1 unit increase in x, demonstrating the linear relationship between the points.