Question 1

Slope = 2 for a line on a graph with x on the horizontal axis and y on the vertical axis.If x decreases by 4, what happens to y?

Accepted Answer

The slope of a line is defined as the change in y divided by the change in x. A slope of 2 means that for every 1 unit decrease in x, y decreases by 2 units. Therefore, if x decreases by 4 units, y decreases by 2*4 = 8 units.

Question 2

The cost of producing copper tubing is $1 per metre.Production costs are measured on the vertical axis and quantity of copper tubing is measured on the horizontal axis.Which of the following would have the smallest slope?

Accepted Answer

The slope of a line on a graph represents the rate of change. When the quantity of copper tubing is measured in millimetres, the scale is much smaller than when measured in metres, centimetres, or decimetres. This means for the same cost increase, the quantity measured in millimetres would increase by a larger amount compared to the other units, resulting in a flatter (smaller slope) line on the graph.

Question 3

Which of the following is an economic application of the slope of a line?

Accepted Answer

The slope of a line can be used in marginal analysis, which involves examining the incremental changes in costs and benefits associated with changes in production or consumption levels.

Question 4

How many economic variables are involved in the relationship reflected on most economics graphs?

Accepted Answer

Most economics graphs only involve two variables, such as supply and demand, price and quantity, or inflation and unemployment. However, some graphs may involve more than two variables in certain situations.

Question 5

What does the statement "There is an inverse relationship between x and y" mean?

Accepted Answer

An inverse relationship means that as one variable (x) increases, the other variable (y) decreases, and vice versa. Therefore, x and y move in opposite directions. It does not necessarily mean that one variable causes the other.

Question 6

Exhibit 1A-5
 
-Refer to the exhibit.According to the curve, if P = $8 then what is Q equal to?

Accepted Answer

At P = $8, the corresponding point on the curve indicates that Q = 8.

Question 7

Which of the following best describes the slope of a horizontal line?

Accepted Answer

A horizontal line has no change in y-coordinate for every change in x-coordinate, which means the slope is zero.

Question 8

Which of the following is the best definition of a slope of a line?

Accepted Answer

The slope of a line represents the rate of change in the vertical direction (rise) with respect to the horizontal direction (run). It is calculated by dividing the change in vertical direction by the change in horizontal direction between any two points on the line. So, the correct definition of slope is "the change in the rise divided by the change in the run," which is option B. Option A is incorrect because it gives the slope as a fraction without considering the change between two points. Option C is the reciprocal of the slope and is incorrect. Option D is incorrect because it gives the inverse of the slope (i.e., the reciprocal).

Question 9

What does the origin on a graph represent?

Accepted Answer

The origin on a graph represents the point at which the values of both variables are zero. It is denoted by the intersection of the x-axis and the y-axis. Thus, option D is the correct choice.

Question 10

Ron weighs 70 kilograms.A graph relates Ron's weight on the vertical axis to Nancy's consumption of ice cream on the horizontal axis.Which statement describes the line on the graph?

Accepted Answer

The line is horizontal at weight = 70 because Ron's weight is constant at 70 kilograms, regardless of Nancy's ice cream consumption, which is represented on the horizontal axis.

Question 11

Exhibit 1A-7
 
-Refer to the exhibit.What is the slope of the line?

Accepted Answer

The answer of Exhibit 1A-7
 
-Refer to the exhibit.What is...

Question 12

A graph shows Ron's weight on the vertical axis and his consumption of ice cream on the horizontal axis.Suppose the graph indicates that for each serving of ice cream he eats, Ron gains 2 kilograms, regardless of how much ice cream he had already eaten.What would this graph show?

Accepted Answer

The graph would show a straight line with a positive slope of 2. This means that for each unit increase in ice cream consumption (horizontal axis), Ron's weight increases by 2 units (vertical axis). The slope of the line represents the rate of change of weight with respect to ice cream consumption, which is constant at 2 in this case.

Question 13

How is the slope of a line defined?

Accepted Answer

The slope of a line represents the rate at which the value of the dependent variable changes with respect to the independent variable. It is defined as the change in the value of the dependent variable (y-axis) divided by the change in the value of the independent variable (x-axis) between any two points on the line. This is commonly referred to as "rise over run" and is represented by the equation:

slope = (y2 - y1) / (x2 - x1)

Question 14

Which of the following best describes the slope of a vertical line?

Accepted Answer

A vertical line has no defined slope because it runs parallel to the y-axis. However, the slope can be described as infinitely large or undefined.

Question 15

Exhibit 1A-8
 $$\begin{array} { c c } 
\mathrm { x } & \mathrm { y } \
\hline 0 & 50 \
100 & 250 \
200 & 450 \
300 & 650 \
400 & 850
\end{array}$$
-Refer to the exhibit.What would the slope of a line graphed with x on the horizontal axis and y on the vertical axis be equal to?

Accepted Answer

To find the slope of a line, we use the formula: 
slope = (change in y) / (change in x)

Using the given data, we can calculate the change in y and change in x between any two points on the line. For example, between the first point (0, 50) and the second point (100, 250): 
change in y = 250 - 50 = 200 
change in x = 100 - 0 = 100

So, the slope between these two points would be: 
slope = (change in y) / (change in x) = 200 / 100 = 2

We can repeat this calculation for any two points on the line and get the same slope of 2. Therefore, we can conclude that the slope of the line is 2.

Question 16

What does the statement "There is a direct relation between x and y" mean?

Accepted Answer

A direct relation between x and y means that when one variable increases, the other also increases, and when one decreases, the other also decreases, indicating they move in the same direction. This statement does not imply causation, only correlation.

Question 17

Exhibit 1A-6
 
-Refer to the exhibit.Which statement best describes the slope of the straight line?

Accepted Answer

The slope of a straight line remains constant throughout its length, meaning it does not change from one point to another on the line.

Question 18

Slope = -2 for a line on a graph with x on the horizontal axis and y on the vertical axis.If x increases by 4, what happens to y?

Accepted Answer

Since the slope of the line is -2, we know that for every increase of 1 in the x-coordinate (horizontal axis), the y-coordinate (vertical axis) decreases by 2. Therefore, if x increases by 4, we expect y to decrease by 8. So the correct answer is D, "y decreases by 8."

Question 19

What is the definition of a graph?

Accepted Answer

A graph is a diagram that shows the relationship between two or more variables. It is a visual representation of data that helps people to understand the information more easily. Other options given in the question (A, C, and D) are incorrect because they do not accurately reflect what a graph is.

Question 20

Exhibit 1A-5
 
-Refer to the exhibit.Which statement best describes line D?

Accepted Answer

Line D shows a negative slope, which indicates an inverse relationship between P and Q. As P decreases, Q increases and vice versa.

Quiz 20: Understanding Graphs