Question

The final cost of a sale item is determined by multiplying the price on the tag by 75%. Which best describes the function that represents the situation? It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant. It is linear because the function is continuous. It is nonlinear because the final cost is determined by multiplying each price tag by 0.75. It is nonlinear because the price tag and final cost columns do not have the same common difference.

Answer 1

First we try to frame the equation between the sale price and the final cost.

Let us consider, the price to be x and the final cost to be y, since the final cost is 75% of the price, we have the below equation

y = 0.75x

This is of the form of straight line equation y = mx +c where c =0 and m = 0.75

This means the function is linear since it satisfies a straight line equation.

So, we can eliminate options (3) and (4)

Now, the function is not a continuous one because the function is has definite value which is 0.75x and this make the function discrete. Hence option (2) is eliminated

Therefore we are left with option (1) which is the answer

Answer is (1) It is linear because the ratio of the change in the final cost compared to the rate of change in the price tag is constant

Answer 2

Let us assume the price on tag is $p and the sale is represented by $s.

It is given that, the price on each tag is multiplied by 75%

$75% = \frac{75}{100} = 0.75$

$s = 0.75\times p$

$s=0.75p$

If we compare this equation with the slope intercept form of line i.e $y=mx+b$

slope m = 0.75 which is constant for all the prices.

Hence, it is clear that the function is linear.

This rejects option C and option D

All linear equations are continuous but we are dealing with the price and sale and price cannot be 0. So we cannot choose option B.

Thus option A is correct .