Question

The table gives the relation between the number of items sold in at a particular time where "x" represents time (in days) and "y" indicates number of items sold.

x	2.5	4	7
y	30	48	84

Which of the following has greater rate of items sold than the table?

• A. y = 13x
• B. y = -20x + 12
• C. y = 12x - 10
• D. y = 10x + 20

Answer 1

The correct option is A y = 13x

Given:

x	2.5	4	7
y	30	48	84

$\text{Rate (Slope)}=\frac{\text{Value of y}}{\text{Value of x}}=\frac{30}{2.5}=12$

We have to find an equation with
$\text{slope}>12.$

In first option:
$\text{Equation is:}y=10x+20$

It in the form of y = mx + c, where m is the slope and c is y-intercept.

∴ Rate (slope) of the equation = 10.

$10<\text{Rate of table.}$

$\text{So,}y=10x+20\text{is not the required equation.}$

In second option:
$\text{Equation is:}y=13x$

It in the form of y = mx, where m is the slope .

∴ Rate (slope) of the equation = 13.

$13>\text{Rate of table.}$

$\text{So,}y=13x\text{is the required equation.}$

In third option:
$\text{Equation is:}y=12x-10$

It in the form of y = mx + c, where m is the slope and c is y-intercept.

∴ Rate (slope) of the equation = 12.

$12=\text{Rate of table.}$

$\text{So,}y=12x-10\text{is not the required equation.}$

In fourth option:
$\text{Equation is:}y=-20x+12$

It in the form of y = mx + c, where m is the slope and c is y-intercept.

∴ Rate (slope) of the equation = -20.

$-20<\text{Rate of table.}$

$\text{So,}y=-20x+12\text{is not the required}$
$\text{equation.}$

$\text{∴}y=13x\text{has a greater rate of item}$
$\text{sold than the table given in question.}$