Question

Use the table of points to answer the following questions. x y −7 5 −3 4 3 5 over 2 Part A: What is the slope from (−7, 5) to (−3, 4)? Show every step of your work. (1 point) Part B: What is the slope from (−3, 4) to 3, five halves? Show every step of your work. (1 point) Part C: What do the slopes from Parts A and B tell you about the relationship between all the points in the table? (2 points)

Answer 1

Part A: The slope from (-7, 5) to (-3, 4) is -1/4. Part B: The slope from (-3, 4) to (3, 5/2) is 1/12. Part C: The different slopes in Parts A and B indicate a non-linear relationship between all the points in the table, suggesting a lack of constant rate of change.

What is slope?

To find slope, use the formula, change in y / change in x.

Part A:

`\[ m = \frac{{4 - 5}}{{-3 - (-7)}} = \frac{{-1}}{{4}} \]`

Part B:

`\[ m = \frac{{(5)/(2) - 4}}{{3 - (-3)}} = \frac{{(1)/(2)}}{{6}} = (1)/(12) \]`

Part C:

The slope from Part A is -1/4, and the slope from Part B is 1/12. Comparing these slopes, we see that the points in the table do not lie on a straight line, as the slopes are different. This suggests that there is no constant rate of change between the points, and the relationship is not linear.