Slope Practice Packet

NAME______#Completed____ #Correct____

Please show all of your work.

1) a) Find the vertical change between the two points on the graph below. b) Find the horizontal change between the two points on the graph below. c) What is the slope of the line? d) What is the y-intercept? e) Write an equation for the line.

2) On the grid above graph a line with a slope of 5. Give two points from your line.

3) On the grid above graph a line with a slope of 1/5. Give two points from your line.

4) Using the two points you found in #2, show how the slope is 5.

5) Using the two points you found in #3, show how the slope is 1/5. 6) Describe what you see in comparing the two lines you drew on the grid. (Please write in complete sentences.) ______

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7) Put these equations in order starting with the most steep. a) y = 3x + 7 b) y = 1/3x + 5 c) y = 1/6x d) y = 3x – 6 e) y = .6x + 5 f) y = 7x + 3 g) y = 2x + 3 h) y = (15/2)x – 2

8) What determines the steepness of a graph? Explain how this affects the steepness. (Please use complete sentences and proper spelling) ______

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9) Using the equation y = 1/2 x + 3 Complete the table below. x y -1 0 1 2 3

10) Using the equation y = 3/2 x + 1/2 Complete the table below. x y -1 0 1 2 3 For numbers 11-15 use the points: (-3, 4) and (3, 3) 11) Find the slope of the line that passes through the points without graphing.

12) Find the y – intercept of the line that passes through the points.

13) Plot the points given above on the above grid. Find the vertical and horizontal distances between the two points and check your answer for #11.

Vertical Distance: Horizontal Distance: Slope:

14) Draw the line that passes through the points and check your answer to #12. Is the y-intercept what you thought it would be. If not, why do you think it is different?

15) Write an equation for the line. Check your equation by plugging in the points and seeing if the equation stays true. (hint: put the x-value for x and the y-value for y). For problems 16 - 20 state which of the following statements is true: (i) The slope is positive (ii) The slope is negative (iii) The slope is zero

(iv) The y-intercept is positive (v) The y-intercept is negative (vi) The y-intercept is zero

(vii) The line passes through the point (1, 4) (viii) The line passes through (3, 4)

16) y = 2x – 2 17) -3x + 7 = y 18) y = 4

19) x -2 0 2 4 6 20) x -3 1 5 7 -7 y 2.5 3.5 4.5 5.5 6.5 y 4 12 20 24 -4

21) A dance club can be rented out for special events or large groups: $100 deposit and $14 a person. The assistant manager decided to give a special rate to his friend for a work party and didn’t tell his boss. When the manager looked at the books he saw that after 10 people entered only $200 had been collected and after 25 had entered, $260 had been collected. Help the manager figure out how much money the assistant manager owes the club. a) Write the two pieces of information as two ordered pair points.

( , ) and ( , ) Plot the points on the grid below. Label the x-axis people and the y-axis money collected. 500 450 400 350 300 250 200 150 100 50

10 20 30 40 50 60 70 80 90 100 .

c) What is the slope of the line? What does it represent in the manager’s investigation?

d) What is the y-intercept of the line? What does it represent?

e) Write an equation for the line and an equation for the original rate. Special Rate:

Normal Rate:

f) If 50 people came to the party, how much money did the club lose? 22) a) Give three possible dimensions for a staircase that has a ratio of .55.

b) Is there a dimension that fits the ratio .55 and also fits the guideline of: rise + run is between 17 and 17.5”? What could it be?