Question

Jaire and Lucy are participating in a push-up challenge.

The table shows the number of push-ups that Jaire can do at the end of each week of the challenge.

Week of challenge Number of push-ups
0 8
2 16
5 28
8 40
The equation y = 4.75x + 5 shows the number of push-ups that Lucy can do at the end of each week of the challenge, with y representing the number of push-ups and x representing the number of weeks.

Which statements about the push-up challenge are true?

Select EACH correct answer.



Lucy does 4.75 more push-ups each week than the previous week.

Jaire does 8 more push-ups each week than the previous week.

Lucy's number of push-ups is increasing at a greater rate than Jaire's number of push-ups.

Lucy can do more push-ups than Jaire at the beginning of the challenge.

Answer 1

Option A is true.
Option B is false.
Option C is true.
Option D is false.
Hope this helps!

Answer 2

The option first and third are correct.

Explanation:

The equation for Lucy push-ups,

`y=4.75x+5`

The slope intercept form of a line is

`y=mx+b`

Where m is the slope.

Therefore the Lucy does 4.75 more push-ups each week than the previous week. The first option is correct.

The table shows the number of push-ups that Jaire can do at the end of each week of the challenge. The tw points from the table are (0,8) and (2,16).

Slope formula is

`m=(y_2-y_1)/(x_2-x_1)`

Slope of the line which passing through (0,8) and (2,16) is

`m=(16-8)/(2-0)=(8)/(2)=4`

Therefore the Jaire does 4 more push-ups each week than the previous week. The second option is incorrect.

The slope represent the rate of change in number of push-ups. The slope of Lucy's push-up equation is more than the slope of Jaire's data.

Therefore Lucy's number of push-ups is increasing at a greater rate than Jaire's number of push-ups. The third option is correct.

The given equation is

`y=4.75x+5`

Put x=0 to find the initial push-ups of Lucy.

`y=4.75(0)+5=5`

In initial the number of Lucy push-ups is 5 and in initial the number of Jaire push-ups is 8 because the table shows the point (0,8).

Therefore, the fourth option is incorrect.