Question

this or that? finding slope
find the slope of each function below and follow the instructions with each correct answer.
1.

x	y
-2	-17
-1	-9
0	-1
1	7
2	15

m = 1/8: write your name at the top of your paper orange
m = 8: write your name backwards at the top of your paper in purple

1. (-3,5) & (6,11)

m = 2/3: draw an orange circle around the hardest question from row 1
m = 2: draw a black circle around the hardest question from row 1

1. (4,-19) & (-2,14)

m = -5/6: draw green zigzags around the hardest question from row 2
m = -11/2: draw purple zigzags around the hardest question from row 2

1. (-6,-2) & (-2,-12)

m = -5/2: draw green dots around the hardest question in row 3
m = 7/2: put orange zigzags around the hardest question in row 3
2.
m = -1/4: shade in quadrant 3 purple
m = -4: shade in quadrant 1 purple
6.

x	y
-12	-12
-6	-11
0	-10
6	-9
12	-8

m = 1/6: shade in every odd box green
m = 8: shade in every odd box orange
10.
m = -2: draw a ghost
m = -1/2: write \boo!\ in bubble letters
14.
m = 4: draw a 3 - eyed monster
m = 1/4: draw a 1 - eyed monster

1. (-1,9) & (2,-12)

m = -21: draw a flying bat
m = -7: draw a jack - o - lantern
7.
m = 1: shade in quadrant 4 orange
m = -1: shade in quadrant 2 green

1. (-18,4) & (-15,5)

m = 1/3: draw a purple bat above the word \that\
m = 3: draw a purple bat above the word \this\
15.

x	y
-1	4
2	22
5	40
8	58
11	76

m = 6: outline your name in your favorite halloween color
m = 18: draw a spiderweb next to your name
4.
m = 4: put an exclamation point after the wordslope
m = 5: put a question mark after the wordslope
8.

x	y
1	-11
3	-7
5	-3
7	1
9	5

m = 4: draw a scary spider
m = 2: draw a nice spider
12.

x	y
-3	25
-2	14
-1	3
0	-8
1	-19

m = -11: shade in every even question orange
m = -8: shade in every even question purple
16.
m = 3: draw a ⊙ next to every question you feel confident on
m = -2: draw a ⊙ next to every question you are unsure on

Explanation:

Step1: Recall slope - formula

The slope formula for two points \((x_1,y_1)\) and \((x_2,y_2)\) is \(m=\frac{y_2 - y_1}{x_2 - x_1}\). For a table of values, we can choose any two points. For a graph, we can identify two points on the line.

Step2: Solve for problem 1

Let's take two points from the table \((x_1,y_1)=(-2,-17)\) and \((x_2,y_2)=(-1,-9)\). Then \(m=\frac{-9-(-17)}{-1 - (-2)}=\frac{-9 + 17}{-1+2}=\frac{8}{1}=8\).

Step3: Solve for problem 2

On the graph, we can identify two points, say \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(4,2)\). Then \(m=\frac{2 - 3}{4-0}=\frac{-1}{4}=-\frac{1}{4}\).

Step4: Solve for problem 3

Given \((x_1,y_1)=(-1,9)\) and \((x_2,y_2)=(2,-12)\), \(m=\frac{-12 - 9}{2-(-1)}=\frac{-21}{3}=-7\).

Step5: Solve for problem 4

On the graph, if we take two points \((x_1,y_1)=(0, - 1)\) and \((x_2,y_2)=(1,3)\), then \(m=\frac{3-(-1)}{1 - 0}=\frac{3 + 1}{1}=4\).

Step6: Solve for problem 5

Given \((x_1,y_1)=(-3,5)\) and \((x_2,y_2)=(6,11)\), \(m=\frac{11 - 5}{6-(-3)}=\frac{6}{9}=\frac{2}{3}\).

Step7: Solve for problem 6

Take two points from the table \((x_1,y_1)=(-12,-12)\) and \((x_2,y_2)=(-6,-11)\), \(m=\frac{-11-(-12)}{-6-(-12)}=\frac{-11 + 12}{-6 + 12}=\frac{1}{6}\).

Step8: Solve for problem 7

On the graph, if \((x_1,y_1)=(0,3)\) and \((x_2,y_2)=(3,0)\), then \(m=\frac{0 - 3}{3-0}=\frac{-3}{3}=-1\).

Step9: Solve for problem 8

Take two points from the table \((x_1,y_1)=(1,-11)\) and \((x_2,y_2)=(3,-7)\), \(m=\frac{-7-(-11)}{3 - 1}=\frac{-7 + 11}{2}=\frac{4}{2}=2\).

Step10: Solve for problem 9

Given \((x_1,y_1)=(4,-19)\) and \((x_2,y_2)=(-2,14)\), \(m=\frac{14-(-19)}{-2 - 4}=\frac{14 + 19}{-6}=\frac{33}{-6}=-\frac{11}{2}\).

Step11: Solve for problem 10

On the graph, if \((x_1,y_1)=(0,4)\) and \((x_2,y_2)=(2,0)\), then \(m=\frac{0 - 4}{2-0}=\frac{-4}{2}=-2\).

Step12: Solve for problem 11

Given \((x_1,y_1)=(-18,4)\) and \((x_2,y_2)=(-15,5)\), \(m=\frac{5 - 4}{-15-(-18)}=\frac{1}{3}\).

Step13: Solve for problem 12

Take two points from the table \((x_1,y_1)=(-3,25)\) and \((x_2,y_2)=(-2,14)\), \(m=\frac{14 - 25}{-2-(-3)}=\frac{14 - 25}{-2 + 3}=-11\).

Step14: Solve for problem 13

Given \((x_1,y_1)=(-6,-2)\) and \((x_2,y_2)=(-2,-12)\), \(m=\frac{-12-(-2)}{-2-(-6)}=\frac{-12 + 2}{-2 + 6}=\frac{-10}{4}=-\frac{5}{2}\).

Step15: Solve for problem 14

On the graph, if \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,4)\), then \(m=\frac{4-0}{1-0}=4\).

Step16: Solve for problem 15

Take two points from the table \((x_1,y_1)=(-1,4)\) and \((x_2,y_2)=(2,22)\), \(m=\frac{22 - 4}{2-(-1)}=\frac{18}{3}=6\).

Step17: Solve for problem 16

On the graph, if \((x_1,y_1)=(0,0)\) and \((x_2,y_2)=(1,3)\), then \(m=\frac{3-0}{1-0}=3\).

Answer:

1. \(m = 8\)
2. \(m=-\frac{1}{4}\)
3. \(m=-7\)
4. \(m = 4\)
5. \(m=\frac{2}{3}\)
6. \(m=\frac{1}{6}\)
7. \(m=-1\)
8. \(m = 2\)
9. \(m=-\frac{11}{2}\)
10. \(m=-2\)
11. \(m=\frac{1}{3}\)
12. \(m=-11\)
13. \(m=-\frac{5}{2}\)
14. \(m = 4\)
15. \(m = 6\)
16. \(m = 3\)