Question

Find the change in y and change in x for any two consecutive points in the graph above. Then enter the rate of change for this line, Change in y (rise) 1 Change in x (run) Rate of change (slope).

Answer 1

For any two consecutive points on the graph, the change in y (rise) is 3, and the change in x (run) is 2. Therefore, the rate of change (slope) is 3/2.

Step-by-step explanation:

To find the change in y and change in x between two consecutive points on the graph, we can choose any two points and calculate the differences in their y-coordinates and x-coordinates. Let's consider two points (x₁, y₁) and (x₂, y₂). The change in y is given by
`\( \Delta y = y₂ - y₁ \)` and the change in x is given by
`\( \Delta x = x₂ - x₁ \).`

In this case, if we select two consecutive points and find the differences in their y-coordinates and x-coordinates, let's say (x₁, y₁) and (x₂, y₂) with values (2, 5) and (4, 8), then the change in y is
`\( \Delta y = 8 - 5 = 3 \)`and the change in x is
`\( \Delta x = 4 - 2 = 2 \).`

The rate of change, or slope, is calculated as the ratio of the change in y to the change in x:
`\( \text{Rate of change} = (\Delta y)/(\Delta x) = (3)/(2) \)`. Therefore, the slope of the line is 3/2, indicating that for every 2 units of horizontal movement (run), there is a corresponding vertical change (rise) of 3 units.

In conclusion, the rate of change (slope) for the given line is 3/2, demonstrating the relationship between the changes in y and x for any two consecutive points on the graph.