Question

Part 1. This is the graph of y=1/2x+10. Use the graph to show that equal intervals of x-values have equal differences of y-values.

Part A of part 1.
Table # 1 y=-1/2(6)+10=____
Table #2 Y=-1/2(10)+10=___
Difference =__
Difference =__
Part B of part 1
Difference in x-values for each interval is ___.
Difference =(p+k)=___.
Part C of part 1
The difference in the y-values for each interval is ___.
Part D of part 1
Does your answer in part C depend on p? If not what does it depend on?

Answer 1

A. y = 7 and y = 5, Difference is 4 and -2 respectively

B. Difference is 4 and (p+k)-p = k

C. Difference is -2

D. Answer in part C does not depend on 'p' but it depends on 'k'.

Explanation:

We have
`y=(-1)/(2)x+10`.

Part A. Now, the values of y are:

Table 1:
`y=(-1)/(2)* 6+10` i.e.
`y=-3+10` i.e. y = 7

Table 2:
`y=(-1)/(2)* 10+10` i.e.
`y=-5+10` i.e. y = 5

Thus, in Table 2, the difference in x-axis = 14-10 = 4 and the difference in y-axis = 3-5 = -2.

Part B. The difference in x-values for each interval is 4.

The value is constant because = (p+k)-p = p+k-p = k.

Part C. The difference in x-values for each interval is -2.

Part D. As, the difference for y-values is
`(-k)/(2)`.

So, we get that the answer in part C does not depend on 'p' but it depends on the value of 'k'.