Section 3.1 – Relations

1. The ___________________ axis can be also called the x-axis.

The horizontal axis is also known as the x-axis because it represents the values of the independent variable in a graph. The x-axis is typically drawn horizontally across the bottom of the graph and is used to measure and display the values of the variable being studied. It is called the horizontal axis because it runs horizontally from left to right.

Explanation

The horizontal axis is also known as the x-axis because it represents the values of the independent variable in a graph. The x-axis is typically drawn horizontally across the bottom of the graph and is used to measure and display the values of the variable being studied. It is called the horizontal axis because it runs horizontally from left to right.

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2. When the graph of a relation is a straight line, the relationship is called __________

When the graph of a relation is a straight line, it means that there is a constant rate of change between the variables. This type of relationship is called linear because it follows a straight line pattern. In a linear relationship, as one variable increases, the other variable also increases or decreases at a constant rate. This can be represented by a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

Explanation

When the graph of a relation is a straight line, it means that there is a constant rate of change between the variables. This type of relationship is called linear because it follows a straight line pattern. In a linear relationship, as one variable increases, the other variable also increases or decreases at a constant rate. This can be represented by a linear equation in the form y = mx + b, where m is the slope of the line and b is the y-intercept.

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3. Raplh works as a painter and charges $30 for an estimate and $20 / hour for his labour. If someone hires him for 5 hours, how much does he roughly charge?

$140

$135

$130

$125

None of the above

Ralph charges $30 for an estimate and $20 per hour for his labor. If someone hires him for 5 hours, the estimate cost of $30 is added to the labor cost of $20/hour for 5 hours. Therefore, the total charge would be $30 + ($20/hour * 5 hours) = $30 + $100 = $130.

Explanation

Ralph charges $30 for an estimate and $20 per hour for his labor. If someone hires him for 5 hours, the estimate cost of $30 is added to the labor cost of $20/hour for 5 hours. Therefore, the total charge would be $30 + ($20/hour * 5 hours) = $30 + $100 = $130.

4.

Which equation represents the relation shown in the table of values?

Y = -4x - 1

Y = 4x + 1

Y = x + 1

Y = x + 4

The equation y = 4x + 1 represents the relation shown in the table of values because it follows the pattern of increasing the value of y by 4 for every increase of 1 in x, and also includes the initial value of y as 1 when x is 0.

Explanation

The equation y = 4x + 1 represents the relation shown in the table of values because it follows the pattern of increasing the value of y by 4 for every increase of 1 in x, and also includes the initial value of y as 1 when x is 0.

5. Name the quadrant where the x-coordiante is negative and the y-coordinate is positive.

1st quadrant

2nd quadrant

3rd quadrant

4th quadrant

None of the above

The second quadrant is where the x-coordinate is negative and the y-coordinate is positive. In this quadrant, the x-values are less than zero and the y-values are greater than zero.

Explanation

The second quadrant is where the x-coordinate is negative and the y-coordinate is positive. In this quadrant, the x-values are less than zero and the y-values are greater than zero.

6.

The graph above shows the relationship between the side length of a square and the perimeter of the square. Use interpolation to determine the area of a square with a side length 8cm, Which choice represents the area? (let the x-axis represent the side length and the y-axis represent the area)

25 cm^2

49 cm^2

64 cm^2

81 cm^2

not-available-via-ai

Explanation

not-available-via-ai

7. Joe works for Future Shop and fixes TV's. He charges a $50 base fee and then $30 for each hour worked. What would be the dependent variable for this situation?

$50

$30 / hour

Cost

Hours

None of the above

The dependent variable in this situation would be the cost. The cost is dependent on the number of hours worked, as well as the base fee. The base fee of $50 is a fixed cost, while the additional $30 for each hour worked is a variable cost. Therefore, the cost is the dependent variable as it varies depending on the number of hours worked.

Explanation

The dependent variable in this situation would be the cost. The cost is dependent on the number of hours worked, as well as the base fee. The base fee of $50 is a fixed cost, while the additional $30 for each hour worked is a variable cost. Therefore, the cost is the dependent variable as it varies depending on the number of hours worked.

8. Susie works at a clothing store and earns a base salray of $100 per week. She also makes $2.00 commision for every article of clothing she sells. What would the equation be to represent her weekly pay if "E" represents her earnings per week and "c" represents every artical of clothing she sells?

E = 2c + 100

E = 100c + 2

E = 100 + 0.2c

E = 2 + 100c

None of the above

The equation E = 2c + 100 represents Susie's weekly pay. The variable "E" represents her earnings per week, and "c" represents the number of articles of clothing she sells. The equation indicates that her earnings consist of a base salary of $100 per week plus a commission of $2.00 for every article of clothing she sells.

Explanation

The equation E = 2c + 100 represents Susie's weekly pay. The variable "E" represents her earnings per week, and "c" represents the number of articles of clothing she sells. The equation indicates that her earnings consist of a base salary of $100 per week plus a commission of $2.00 for every article of clothing she sells.

9.

Which equation represents the relation shown on the graph?

Y = -2x + 4

Y = 2x + 4

Y = x + 4

Y = -x + 4

The equation y = 2x + 4 represents the relation shown on the graph because it has a slope of 2, indicating that the line rises 2 units for every 1 unit it moves to the right. The y-intercept is 4, indicating that the line intersects the y-axis at the point (0, 4). This matches the behavior of the line on the graph, which rises at a steep slope of 2 and intersects the y-axis at y = 4.

Explanation

The equation y = 2x + 4 represents the relation shown on the graph because it has a slope of 2, indicating that the line rises 2 units for every 1 unit it moves to the right. The y-intercept is 4, indicating that the line intersects the y-axis at the point (0, 4). This matches the behavior of the line on the graph, which rises at a steep slope of 2 and intersects the y-axis at y = 4.

10. Which of these ordered pairs are points on the graph of y = -5x + 2

(1, 3)

(-1, 7)

(-2, -8)

(4, 22)

The correct answer is (-1, 7) because when we substitute x = -1 into the equation y = -5x + 2, we get y = -5(-1) + 2 = 7. Therefore, the ordered pair (-1, 7) is a point on the graph of y = -5x + 2.

Explanation

The correct answer is (-1, 7) because when we substitute x = -1 into the equation y = -5x + 2, we get y = -5(-1) + 2 = 7. Therefore, the ordered pair (-1, 7) is a point on the graph of y = -5x + 2.

11.

Which equation represents the relation shown in the table of values?

Y = x + 10

Y = -3x - 4

Y = 3x + 4

Y = -3x + 4

The equation y = -3x + 4 represents the relation shown in the table of values because it follows the pattern of the given values. When x = 0, y = 4, and when x = 1, y = 1, which matches the values in the table. Additionally, the equation has a slope of -3, which is consistent with the rate of change in the table.

Explanation

The equation y = -3x + 4 represents the relation shown in the table of values because it follows the pattern of the given values. When x = 0, y = 4, and when x = 1, y = 1, which matches the values in the table. Additionally, the equation has a slope of -3, which is consistent with the rate of change in the table.

12. Which of these ordered pairs are points on the graph of y = 3x - 6

(2, 1)

(-3, 3)

(-1, -3)

(6, 12)

The ordered pair (6, 12) is a point on the graph of y = 3x - 6 because when we substitute x = 6 into the equation, we get y = 3(6) - 6 = 18 - 6 = 12. Therefore, the point (6, 12) satisfies the equation and lies on the graph.

Explanation

The ordered pair (6, 12) is a point on the graph of y = 3x - 6 because when we substitute x = 6 into the equation, we get y = 3(6) - 6 = 18 - 6 = 12. Therefore, the point (6, 12) satisfies the equation and lies on the graph.

13.

The graph above shows the relationship between the earnings Jay received and the hours be worked per week. Use interpolation to determine the earnings Jay received for working 20 hours. Which choice represents the earnings? (let the x-axis represent hours worked and the y-axis represent the his earnings)

$175

$190

$200

$225

The graph above shows the relationship between Jay's earnings and the hours he worked per week. By using interpolation, we can estimate Jay's earnings for working 20 hours. Looking at the graph, we can see that the line connecting the points for 15 hours and 25 hours intersects with the y-axis at approximately $190. Therefore, the correct answer is $190.

Explanation

The graph above shows the relationship between Jay's earnings and the hours he worked per week. By using interpolation, we can estimate Jay's earnings for working 20 hours. Looking at the graph, we can see that the line connecting the points for 15 hours and 25 hours intersects with the y-axis at approximately $190. Therefore, the correct answer is $190.

14.

Which equation represents the relation shown on the graph?

Y = -2x + 18

Y = 2x + 18

Y = -4x + 18

Y = 4x + 18

The equation y = -4x + 18 represents the relation shown on the graph because it has a negative slope of -4, which matches the steepness of the line on the graph. The y-intercept of 18 also matches the point where the line intersects the y-axis on the graph. Therefore, this equation accurately represents the relationship between x and y shown on the graph.

Explanation

The equation y = -4x + 18 represents the relation shown on the graph because it has a negative slope of -4, which matches the steepness of the line on the graph. The y-intercept of 18 also matches the point where the line intersects the y-axis on the graph. Therefore, this equation accurately represents the relationship between x and y shown on the graph.