Question

Identify the correct relation between the number of teams and the number of coaches.

Number of teams (x)	5	7	10
Number of coaches (y)	13	17	23

• A. $y=2x-3$
• B. $y=2x+3$
• C. $y=x+8$
• D. $y=x+10$

Answer 1

The correct option is B $y=2x+3$

We have to match the values of x (by substituting them in the given options) to the values of y, given in the table.

For the first option: $y=2x-3$, by substituting values of x, we get:

Number of teams (x)	$5$	$7$	$10$
$y=2x-3$	$2\times 5-3$ $=10-3$ $=7$	$2\times 7-3$ $=14-3$ $=11$	$2\times 10-3$ $=20-3$ $=17$
Number of coaches (y)	$7$	$11$	$17$

We see that the values of y obtained, do not match with the values given in the table.

For the second option: $y=2x+3$, by substituting values of x, we get:

Number of teams (x)	$5$	$7$	$10$
$y=2x+3$	$2\times 5+3$ $=10+3$ $=13$	$2\times 7+3$ $=14+3$ $=17$	$2\times 10+3$ $=20+3$ $=23$
Number of coaches (y)	$13$	$17$	$23$

We see that the values of y obtained, exactly matches with the values given in the table.

For the third option: $y=x+8$, by substituting values of x, we get:

Number of teams (x)	$5$	$7$	$10$
$y=x+8$	$5+8$ $=13$	$7+8$ $=15$	$10+8$ $=18$
Number of coaches (y)	$13$	$15$	$18$

We see that the values of y obtained, do not match with the values given in the table.

For the fourth option: $y=x+10$, by substituting values of x, we get:

Number of teams (x)	$5$	$7$	$10$
$y=x+10$	$5+10$ $=15$	$7+10$ $=17$	$10+10$ $=20$
Number of coaches (y)	$15$	$17$	$20$

So, we see that the correct relationship of x and y for the table given is: $y=2x+3$