Questions

1) Print out or copy the given table. For the function y = x – 3, find the y-values for the x-values provided in the chart. On graph paper, graph the ordered pairs. (a) State the five ordered pairs and (b) describe the type of graph that is formed when the points are connected.

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2) Print out the table. For the function y = 3x + 2, find the y-values for the x-values provided in the chart. On graph paper, graph the ordered pairs. (a) State the five ordered pairs and (b) describe the type of graph that is formed when the points are connected.

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3) List three ordered pairs for the dark points (red) that fall on the graphed line.

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4) Which equation could be used to represent the relationship of “x” and “y” for the ordered pairs found in the previous problem? (Hint: Substitute the x-value of a few of the points into the equation and solve for the corresponding y-values.)

a.) y = –3x

b.) y = 3x

c.) y = –3x – 1

d.) y = 3x – 1

5) Consider other points that fall on the line and fall away from the line and which ones fit the equation above? The diamond (yellow) point and the triangle (blue) point are provided to use as a test points. Is the following conjecture true or false? Please give a rationale to support the answer. In the rationale, include how the diamond and triangle points do or do not fit the equation.

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6) What are the x- and y-intercepts of the equation, 3x + 4y = 12. (Note: The intercepts are written as ordered pairs.)

a.) x-intercept (–3, 0), y-intercept (0, 4)

b.) x-intercept (4, 0), y-intercept (0, 3)

c.) x-intercept (3, 0), y-intercept (0, –4)

d.) x-intercept (–4, 0), y-intercept (0, –3)

7) On graph paper, graph the equation of 3x + 4y = 12 using the x- and y-intercepts. State the letter of the correct answer.

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8) On graph paper, graph the equation of 5x – 2y = 10 using the x- and y-intercepts. State the (a) letter of the correct graph and (b) the coordinates of the x- and y-intercepts.

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9) Which of the follow statements is a true general statement about the x- and y-intercepts?

a.) For the x-intercept, the x-coordinate of its ordered pair is always 0. For the y-intercept, the y-coordinate of its ordered pair is always 0.

b.) For the x-intercept, the y-coordinate of its ordered pair is always 0. For the y-intercept, the x-coordinate of its ordered pair is always 0.

c.) For the x-intercept, the x-coordinate of its ordered pair is not 0. For the y-intercept, the y-coordinate of its ordered pair is always 0.

d.) For the x-intercept, the y-coordinate of its ordered pair is not 0. For the y-intercept, the x-coordinate of its ordered pair is always 0.

10) What is the slope of the line graphed below?

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11) What is the slope of the line graphed below?

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12) Consider points Q(–5, 6) and R(5, –1) on line QR. What is the slope of the line? State the letter of the correct solution for calculating the slope.

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13) What is the slope of the wakeboard?

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14) What is the slope of the linear graph?

a.) The slope of the line is zero. (0 / –5 = 0)

b.) The slope of the line is undefined. (–5 / 0 has no answer.)

15) What is the slope of the linear graph?

a.) The slope of the line is zero. (0 / 6 = 0)

b.) The slope of the line is undefined. (6 / 0 has no answer.)

16) On graph paper, graph the line containing the point (–3, –4) and has a slope of m = 1/2. To demonstrate that the graph is correct, locate the x-intercept. What are the coordinates of the x-intercept?

a.) (0, 5)

b.) (5, 0)

c.) (0, –5)

d.) (–5, 0)

17) On graph paper, graph the line containing the point (–5, 1) and has a slope of m = –2/3. To demonstrate that the graph is correct, locate the x-intercept. What are the coordinates of the x-intercept?

a.) (0, 3 1/2)

b.) (3 1/2, 0)

c.) (0, –3 1/2)

d.) (–3 1/2, 0)

18) Compare the slopes of the two lines. If a person were able to climb the two lines from the bottom right to the upper left, which line would be steeper to climb?

a.) Line “r” is steeper than line “s”.

b.) Line “s” is steeper than line “r”.

19) Study the graphs of the given equations and the given statement. Pay close attention to the incline or decline of the graphed lines and how this corresponds with the numerical value of the slope (m) in the equation. Which term in parenthesis completes the statement correctly? (Note: In these equations, the y-intercept is zero.)

a.) flatter

b.) steeper

20) Study the graphs of the given equations and the given statements. Pay close attention to what varies and what stays the same. Which terms in parenthesis complete the statements correctly in the order given?

a.) different, different

b.) different, the same

c.) the same, different

d.) the same, the same

21) Refer to the previous problem to complete the following statement. When the slopes of linear equations are the same, the lines of the linear graphs:

a.) are perpendicular.

b.) are parallel.

c.) are the same line.

d.) have no apparent relationship.

22) Study the graphs of the given equations and the given statements. Pay close attention to what varies and what stays the same. Which terms in parenthesis complete the statements correctly in the order given?

a.) different, different

b.) different, the same

c.) the same, different

d.) the same, the same

23) The distance a wake boarder travels is recorded in the graph below. The graph is linear; thus, his speed is directly related to the slope of the graph. Calculate the wake boarder’s speed using the slope formula. Express the answer in feet per second.

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24) The graph below represents the sound of thunder after a lightning bolt struck a nearby tree. Tonya, who lives closer to the tree, heard the lightening 2.5 seconds after the lightning bolt struck the nearby tree. Darren, who lives farther from the tree, heard the thunder 6 seconds after the lightning struck the tree. Find the rate (ft/s) the sound of thunder was traveling.

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25) What is the speed of the ski lift? (Note: Use the change in altitudes and times of any two persons shown in the chart.)

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26) What is an equation in slope-intercept form that represents the relationship of the data provided in the chart and graph? (Slope-Intercept Form: y = mx + b)

a.) y = 6250x + 130

b.) y = 6380x

c.) y = 130x

d.) y = 130x + 6250

27) If Lori had 12 tables of customers, predict how much money in tips she would receive?

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28) Predict how many hours Lori would have to work to receive $80 in tips?

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29) A paramotor is a parachute propelled by a fan-like motor. After reaching a height of 2000 feet, a paramotorist descends an average rate of 250 feet per minute. After 1 minute, the paramotorist has an altitude of 1750 feet. After 2 minutes, the paramotorist has an altitude of 1500 feet. After 3 minutes, the paramotorist has an altitude of 1250 feet. Predict how many minutes it will take the paramotorist to reach the ground?

a.) 5 minutes

b.) 6 minutes

c.) 7 minutes

d.) 8 minutes

30) Describe a “real-life” example of direct variation; that is, one quantity varies directly as the other quantity changes.

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31) If y varies directly as x, and y = 27 when x = 9, find the constant of the variation and write an equation of direct variation.

a.) k = 81, y = 81x

b.) k = 27, y = 27x

c.) k = 9, y = 9x

d.) k = 3, y = 3x

32) If y varies directly as x, and y = 48 when x = 6, find the constant of the variation and write an equation of direct variation.

a.) k = 8, y = 8x

b.) k = 336, y = 336x

c.) k = 6, y = 6x

d.) k = 48, y = 48x

33) If the miles traveled (m) varies directly to the amount of gasoline used (g), and m = 223 miles when g = 10 gallons, (a) what is the constant of variation and (b) what is the equation of direct variation?

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