Question

In 6-8 each table represents a linear relationship. Use the slope formula to find the slope or rate of change shown in each table 6: x: 2,6,10,14 y:8,28,48,68

7: x -6,4,9,20 y:5,10,12.5,18

Answer 1

The slope for Table 6 is 5, calculated by using two points from the table and applying the slope formula. For Table 7, the slope is 0.5, following the same process of picking two points and calculating the rate of change between them.

Step-by-step explanation:

The task is to calculate the slope or rate of change for two linear relationships represented by two tables. The slope, often denoted as 'm', is calculated by the formula:

slope (m) = (change in y) / (change in x) = ∆y / ∆x

For Table 6:

• Select two points, for example: (2, 8) and (14, 68).
• Calculate the differences in y and x values: ∆y = 68 - 8, ∆x = 14 - 2.
• Compute the slope: m = ∆y / ∆x = 60 / 12 = 5.

For Table 7:

• Select two points, for example: (-6, 5) and (20, 18).
• Calculate the differences in y and x values: ∆y = 18 - 5, ∆x = 20 - (-6).
• Compute the slope: m = ∆y / ∆x = 13 / 26 = 0.5.

The slope for Table 6 is 5 and Table 7 is 0.5.