Algebra 2: Sect. 1.1 - 1.2 Test

1. Question E

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2. Question M
Using the equation y = -4x - 2, what will be the y-coordinate of a point whose x coordinate is 5?

-11

18

-22

12

The equation y = -4x - 2 represents a linear function in slope-intercept form, where the coefficient of x is the slope and the constant term is the y-intercept. In this case, the slope is -4 and the y-intercept is -2. To find the y-coordinate of a point with x = 5, we substitute x = 5 into the equation: y = -4(5) - 2 = -20 - 2 = -22. Therefore, the y-coordinate of the point is -22.

Explanation

The equation y = -4x - 2 represents a linear function in slope-intercept form, where the coefficient of x is the slope and the constant term is the y-intercept. In this case, the slope is -4 and the y-intercept is -2. To find the y-coordinate of a point with x = 5, we substitute x = 5 into the equation: y = -4(5) - 2 = -20 - 2 = -22. Therefore, the y-coordinate of the point is -22.

3. Question C
A family membership at a swimming pool costs a flat fee of $100, plus $50 per person. If the letter n stands for the number of people, and C is the total cost, then the equation that best describes this situation is:
A) C = 50n + 100
B) C = 100n + 50
C) C = 100 + 50 + n
D) C = 150n

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B

C

D

The equation that best describes the situation is C = 50n + 100. This is because there is a flat fee of $100, which is added to the cost of $50 per person (n). Therefore, the total cost (C) is calculated by multiplying the number of people (n) by $50 and adding the flat fee of $100.

Explanation

The equation that best describes the situation is C = 50n + 100. This is because there is a flat fee of $100, which is added to the cost of $50 per person (n). Therefore, the total cost (C) is calculated by multiplying the number of people (n) by $50 and adding the flat fee of $100.

4. Question L

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5. Question N
Using the graph below, determine the slope of this line:

-3/6

3/5

-2/6

2/5

The slope of a line is determined by the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points on the line. In this case, the line passes through the points (0, -3) and (5, 3). The change in the y-coordinates is 3 - (-3) = 6, and the change in the x-coordinates is 5 - 0 = 5. Therefore, the slope of the line is 6/5, which is equivalent to 2/5.

Explanation

The slope of a line is determined by the ratio of the change in the y-coordinates to the change in the x-coordinates between any two points on the line. In this case, the line passes through the points (0, -3) and (5, 3). The change in the y-coordinates is 3 - (-3) = 6, and the change in the x-coordinates is 5 - 0 = 5. Therefore, the slope of the line is 6/5, which is equivalent to 2/5.

6. Question H

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7. Question B

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8. Question G

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9. Question A
Which of these points does not lie on the graph of y = -3x - 4?
A) (0 , -4)
B) (1 , -1)
C) (-1 , -1)
D) (-2 , 2)

A

B

C

D

The point (1, -1) does not lie on the graph of y = -3x - 4 because when we substitute x = 1 into the equation, we get y = -3(1) - 4 = -3 - 4 = -7, not -1.

Explanation

The point (1, -1) does not lie on the graph of y = -3x - 4 because when we substitute x = 1 into the equation, we get y = -3(1) - 4 = -3 - 4 = -7, not -1.

10. Question D

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11. Question P
Change the equation -3x + 5y = 10 into slope-intercept form.

5y = 3x + 10

Y = 3x + 10

Y = 3/5 x + 2

Y = 5/3 x + 10/3

The equation -3x + 5y = 10 is converted into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By rearranging the equation, we can isolate y on one side. The correct answer, y = 3/5 x + 2, shows that the slope is 3/5, indicating that for every increase of 1 in x, y increases by 3/5. The y-intercept is 2, meaning that the line crosses the y-axis at the point (0, 2). Thus, the equation is in slope-intercept form.

Explanation

The equation -3x + 5y = 10 is converted into slope-intercept form, y = mx + b, where m is the slope and b is the y-intercept. By rearranging the equation, we can isolate y on one side. The correct answer, y = 3/5 x + 2, shows that the slope is 3/5, indicating that for every increase of 1 in x, y increases by 3/5. The y-intercept is 2, meaning that the line crosses the y-axis at the point (0, 2). Thus, the equation is in slope-intercept form.

12. Question F

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13. Question K

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14. Question O
What is the equation of the line below in y = mx + b form?

Y = -2x

Y= -1/2 x + 1

Y = -1/2 x + 2

Y = 1/2 x + 1

The equation of the line in y = mx + b form is y = -1/2x + 1 because it follows the standard form of a linear equation. The coefficient of x, -1/2, represents the slope of the line, which indicates that the line is decreasing as x increases. The constant term, 1, represents the y-intercept, which is the point where the line crosses the y-axis. Therefore, the equation y = -1/2x + 1 accurately represents the given line.

Explanation

The equation of the line in y = mx + b form is y = -1/2x + 1 because it follows the standard form of a linear equation. The coefficient of x, -1/2, represents the slope of the line, which indicates that the line is decreasing as x increases. The constant term, 1, represents the y-intercept, which is the point where the line crosses the y-axis. Therefore, the equation y = -1/2x + 1 accurately represents the given line.

15. Question J

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