Question 1

An economist observed that, as more computers are added to a factory, the costs of production initially decline, reach a minimum, and then rise. In a diagram that has costs on the vertical axis and the number of computers on the horizontal axis, the relationship always is

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The answer of An economist observed that, as more computers...

Question 2

On a graph showing the relationship between x and y, the ceteris paribus condition implies that

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The answer of On a graph showing the relationship between...

Question 3

If a curve falls and then rises, it

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When a curve falls and then rises, it indicates the presence of a minimum point, where the value of the function is at its lowest in the local vicinity.

Question 4

The slope of a line equals the change in the variable measured along the

Accepted Answer

The slope of a line is defined as the change in the variable measured along the y-axis divided by the change in the variable measured along the x-axis, which is represented by the equation: 
slope = (change in y)/(change in x) 
Therefore, the best choice is E, as it states that the slope equals the y-axis divided by the change in the variable measured along the x-axis.

Question 5

Which of the following statements is correct?

Accepted Answer

A straight line with an upward slope moving to the right always has a positive slope. The other statements are incorrect. The slope of a straight line is constant, and the slope of a curved line can be calculated using calculus.

Question 6

A graph shows that the number of Australian tourists visiting a Caribbean island increases as the temperature in southern Australia falls. The graph shows

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The answer of A graph shows that the number of...

Question 7

If the quantity of the variable on the y-axis increases by 10 when the quantity of the variable on the x-axis decreases by 2, then the slope of the curve equals

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The slope of a curve is defined as the change in the vertical variable (y-axis) per unit change in the horizontal variable (x-axis).

Given that the quantity of the variable on the y-axis increases by 10 when the quantity of the variable on the x-axis decreases by 2, we can say that:

Slope = Change in y / Change in x

Slope = 10 / (-2) [Note: Decrease in x-axis is represented as -2]

Slope = -5

Therefore, the slope of the curve is -5, and the correct choice is C.

Question 8

When two variables in a graph are related to a third, changing the third causes

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The answer of When two variables in a graph are...

Question 9

A curve with a positive but decreasing slope represents a relationship where, every time the variable measured along the horizontal axis increases by one unit, the variable measured along the vertical axis

Accepted Answer

A positive but decreasing slope means that as the value on the x-axis increases by one unit, the value on the y-axis increases but at a decreasing rate. This means that the value on the y-axis is increasing, but the increase is getting smaller for each unit increase on the x-axis. Therefore, the best choice is E, which states that the variable on the y-axis is increasing by a decreasing amount.

Question 10

The figure above shows the relationship between the price of a dozen roses and the quantity of roses a florist can sell. The slope between points A and B is

Accepted Answer

The slope of a line represents the change in y (quantity of roses) for a given change in x (price of roses). To find the slope between points A and B, we need to calculate the rise and the run.

Rise = Change in Quantity = 16 - 8 = 8
Run = Change in Price = $28 - $20 = $8

Therefore, the slope between points A and B is:

slope = rise / run = 8 / 8 = 1

However, the question asks for the slope in dozens of roses (not units), so we need to divide the slope by 12:

slope = 1 / 12 = 1/12 dozen of roses per dollar

Since the slope is given in dozens of roses per dollar, we can also write it as:

slope = 2 dozens of roses for every $24 increase in price

Therefore, the correct choice is B) 2.

Question 11

With y measured on the vertical axis and x measured on the horizontal axis, the slope of a straight line is defined as

Accepted Answer

The slope of a straight line is the ratio of the change in the vertical axis (y) to the change in the horizontal axis (x), which is expressed as (change in y)/(change in x). Therefore, choice A is the correct definition of slope.

Question 12

The Latin term 'ceteris paribus' means

Accepted Answer

'Ceteris paribus' translates to 'other things remaining the same,' and is often used in economics and other social sciences to isolate the effect of one variable on another while holding all other variables constant.

Question 13

The figure above shows the relationship between the price of a dozen roses and the quantity of roses a florist can sell. The slope between points C and D equals

Accepted Answer

The slope of a line is defined as the change in the y-variable divided by the change in the x-variable. From point C to point D, the quantity of roses sold increases from 3 dozen to 11 dozen, a change of 8 dozen. The price of roses decreases from $50 to $10, a change of $40. Therefore, the slope equals -40/8 = -5. However, the question asks for the absolute value of the slope, which is 8.

Question 14

In the above figure, while drawing the line showing the relationship between the price of a kilogram of peanuts and the quantity sold, the

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The answer of In the above figure, while drawing the...

Question 15

A slope is measured as the:

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The slope is defined as the change in the value of the y-variable divided by the change in the value of the x-variable. This can be represented as (y2 - y1) / (x2 - x1), where (x1, y1) and (x2, y2) are two points on the line. Therefore, option B is the correct choice.

Question 16

If the quantity of the variable on the y-axis increases by 3 when the quantity of the variable on the x-axis increases by 4, then the slope of the curve equals

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The answer of If the quantity of the variable on...

Question 17

The above figure shows the relationship between the price of a slice of pizza and how many slices of pizza Ricardo buys in a week. Between points A and B, the slope of the line is ________ the slope of the line between points B and C.

Accepted Answer

The slope of a line is a measure of its steepness. The greater the slope, the steeper the line. In the given figure, the slope of the line between points A and B is less than the slope of the line between points B and C. This is because the line between points A and B is flatter than the line between points B and C.

Question 18

The figure above shows the relationship between the price of a dozen roses and the quantity of roses a florist can sell. The slope between points B and C equals

Accepted Answer

The slope of a line represents the rate of change of one variable with respect to the other variable. In this case, the slope between points B and C is the change in quantity of roses sold divided by the change in price.

From point B to point C, the quantity of roses sold increases from 8 dozen to 16 dozen, which is a change of 8 dozen. The price decreases from $80 to $64, which is a change of $16.

Therefore, the slope between points B and C is:

(change in quantity)/(change in price) = (8 dozen)/($16) = 0.5 dozen/$

Simplifying further, we can express the slope as 4 dozens/$8, which reduces to 0.5 dozen/$.

Therefore, the answer is B) 4.

Question 19

'The change in the value of the variable measured on the y-axis divided by the change in the value of the variable measured on the x-axis' is the definition of

Accepted Answer

The definition given is that of slope, which is a measure of the steepness of a line or curve on a graph.

Question 20

We are investigating the relationship among three variables. We have graphed two of them. Suppose that the variable that is not measured on the x-axis or the y-axis changes. Then, there is

Accepted Answer

When a third variable (not measured on the x- or y-axis) changes and affects the relationship between the two variables being graphed, it can cause a shift in the plotted curve. This is because the third variable might influence the underlying relationship, leading to different outcomes that are reflected as a shift in the curve.

Quiz 1: Getting Started