Question 1

If slope = -2 for a line on a graph with x on the horizontal axis and y on the vertical axis,then if
A)x increases by 4,y increases by 8
B)x increases by 4,y increases by 2
C)y increases by 4,x increases by 8
D)x = 4,y = 8
E)x increases by 4,y decreases by 8

Accepted Answer

The answer of If slope = -2 for a line...

Question 2

Moderate exercise is better than none,but excessive exercise is harmful.What is the shape of the graph of health benefits versus hours of exercise per week if health benefits are measured on the vertical axis and exercise is measured on the horizontal axis?
A)a positively sloped straight line
B)a negatively sloped straight line
C)a vertical straight line
D)a U-shaped curve
E)a hill-shaped curve

Accepted Answer

The answer of Moderate exercise is better than none,but excessive...

Question 3

Suppose a graph with Ron's weight on the vertical axis and his consumption of ice cream on the horizontal axis indicated that for each serving of ice cream he ate,Ron would gain 3 pounds,regardless of how much ice cream he had already eaten.This graph would show a
A)horizontal line at weight = 3
B)straight line with slope = 3
C)straight line with slope = 1/2
D)straight line with slope = -3
E)straight line with slope = -1/3

Accepted Answer

Since for each serving of ice cream, Ron gains 3 pounds, the weight is directly proportional to the number of servings of ice cream. This is represented by a straight line with a slope of 3. Therefore, the correct choice is B.

Question 4

A U-shaped curve has a positive slope everywhere.

Accepted Answer

A U-shaped curve has a negative slope at the top (the bottom of the U) and a positive slope on either side of the bottom.

Question 5

If slope = 2 for a line on a graph with x on the horizontal axis and y on the vertical axis,then if
A)x decreases by 4,y decreases by 8
B)x = -4,then y = -2
C)y decreases by 4,x decreases by 8
D)x = -4,y = -8
E)x increases by 4,y decreases by 8

Accepted Answer

The answer of If slope = 2 for a line...

Question 6

A straight line tangent to a curved line at a point
A)crosses the curved line at that point
B)crosses the curved line at many points
C)has the same slope as the curved line at that point
D)is steeper than the curve at all other points
E)has a smaller slope than all other points on the curve

Accepted Answer

A line tangent to a curved line at a point only touches the curved line at that point without crossing it. The tangent line has the same slope as the curved line at that point, making choice C the best answer. The other choices are incorrect because a tangent line does not cross the curve at many points (B), and it is not necessarily steeper than the curve at all other points (D) or have a smaller slope than all other points on the curve (E).

Question 7

Suppose the cost of producing copper tubing is $1 per foot.If production costs were measured on the vertical axis and quantity of copper tubing were measured on the horizontal axis,which of the following lines would have the smallest slope?
A)a line representing the quantity of tubing measured in inches
B)a line representing the quantity of tubing measured in feet
C)a line representing the quantity of tubing measured in yards
D)the 45-degree line
E)any vertical line

Accepted Answer

The answer of Suppose the cost of producing copper tubing...

Question 8

Exhibit 1-10 
-In Exhibit 1-10,the slope of the line is
A)negative for all values of x
B)positive for all values of x
C)zero at x = 7
D)first negative,then positive as x increases
E)negative for all values of y

Accepted Answer

The answer of Exhibit 1-10 
-In Exhibit 1-10,the slope of...

Question 9

The slope of a U-shaped curve is infinity at the bottom of the U.

Accepted Answer

The answer of The slope of a U-shaped curve is...

Question 10

The slope of an inverted U-shaped curve is infinity at the top of the curve.

Accepted Answer

The slope of an inverted U-shaped curve is zero at the top of the curve, not infinity. Infinity slope would imply that the curve is increasing at an infinitely fast rate at the top, which is not possible.

Question 11

Exhibit 1-8 
-The slope of a vertical line is
A)infinitely large
B)zero
C)positive
D)negative
E)infinitely small

Accepted Answer

A vertical line has an undefined slope because the change in y (vertical) is infinite and the change in x (horizontal) is zero.

Question 12

Ron weighs 150 pounds.A graph relating Ron's weight on the vertical axis to Nancy's consumption of ice cream on the horizontal axis would be
A)a horizontal line at weight = 150
B)a horizontal line at weight = 0
C)a positively sloped line with decreasing slope
D)a vertical line at weight = 150
E)the origin

Accepted Answer

The answer of Ron weighs 150 pounds.A graph relating Ron's...

Question 13

One economic application of the slope of a line is
A)measuring unlimited wants
B)behavioral analysis
C)marginal analysis
D)allocative efficiency
E)rational self-interest

Accepted Answer

The slope of a line can be used to calculate the marginal analysis, which involves analyzing the change in cost or benefit resulting from a small change in production or consumption. It is an essential tool for determining the optimal level of output and pricing and achieving allocative efficiency. Therefore, option C is the correct answer.

Question 14

The numerical value of the slope of a line depends in part on the units of measurement used.

Accepted Answer

The answer of The numerical value of the slope of...

Question 15

The slope of a line
A)can only be calculated for straight lines
B)varies at different points along a straight line
C)indicates whether or not there is a causal relationship between variables
D)is independent of the units of measurement used
E)indicates how much the vertical variable changes for a given change in the horizontal variable

Accepted Answer

The slope of a line measures the rate of change of the vertical variable with respect to the horizontal variable. It indicates how much the vertical variable changes for a given change in the horizontal variable. The slope can be calculated for any type of line, not just straight lines. The slope is not an indication of whether or not there is a causal relationship between variables, and it is affected by the units of measurement used.

Question 16

Exhibit 1-8 
-The slope of the line in Exhibit 1-8 is
A)0.1
B)1
C)10
D)-0.1
E)-10

Accepted Answer

The slope of a line is equal to the rise over the run. In this case, the line has a rise of 1 and a run of 0.1, so the slope is 1/0.1 = 10. Therefore, the answer is C.

Question 17

Exhibit 1-7 
-The slope of the straight line in Exhibit 1-7 is
A)greater at point a than at point b
B)the same at points a and b
C)zero because the line is straight
D)negative because an inverse relation is shown
E)positive because the line lies to the right of the y-axis

Accepted Answer

The slope of a straight line is constant at all points along the line, so it is the same at points a and b.

Question 18

A curved line may have a positive slope or a negative slope,but it cannot have both positive and negative areas of slope.

Accepted Answer

A curved line can have both positive and negative areas of slope. A positive area of slope would indicate that the curve is increasing, while a negative area of slope would indicate that the curve is decreasing.

Question 19

A line is tangent to a curve if it
A)crosses the curve at one point
B)touches the curve at one point,without crossing it
C)crosses the curve at a minimum of two points
D)never touches the curve
E)forms a right triangle with the curve

Accepted Answer

A tangent line to a curve only touches it at one point without crossing it.

Question 20

Exhibit 1-8 
-The slope of a horizontal line is
A)infinitely large
B)zero
C)positive
D)negative
E)infinitely small

Accepted Answer

A horizontal line has a slope of zero.

Quiz 22: understanding Graphs

If slope = -2 for a line on a graph with x on the horizontal axis and y on the vertical axis,then if

Moderate exercise is better than none,but excessive exercise is harmful.What is the shape of the graph of health benefits versus hours of exercise per week if health benefits are measured on the vertical axis and exercise is measured on the horizontal axis?

Suppose a graph with Ron's weight on the vertical axis and his consumption of ice cream on the horizontal axis indicated that for each serving of ice cream he ate,Ron would gain 3 pounds,regardless of how much ice cream he had already eaten.This graph would show a

A U-shaped curve has a positive slope everywhere.

If slope = 2 for a line on a graph with x on the horizontal axis and y on the vertical axis,then if

A straight line tangent to a curved line at a point

Suppose the cost of producing copper tubing is $1 per foot.If production costs were measured on the vertical axis and quantity of copper tubing were measured on the horizontal axis,which of the following lines would have the smallest slope?

Exhibit 1-10 -In Exhibit 1-10,the slope of the line is

The slope of a U-shaped curve is infinity at the bottom of the U.

The slope of an inverted U-shaped curve is infinity at the top of the curve.

Exhibit 1-8 -The slope of a vertical line is

Ron weighs 150 pounds.A graph relating Ron's weight on the vertical axis to Nancy's consumption of ice cream on the horizontal axis would be

One economic application of the slope of a line is

The numerical value of the slope of a line depends in part on the units of measurement used.

The slope of a line

Exhibit 1-8 -The slope of the line in Exhibit 1-8 is

Exhibit 1-7 -The slope of the straight line in Exhibit 1-7 is

A curved line may have a positive slope or a negative slope,but it cannot have both positive and negative areas of slope.

A line is tangent to a curve if it

Exhibit 1-8 -The slope of a horizontal line is