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worksheet 4-01 finding the rule for each of the following tables of val…

Question

worksheet 4-01 finding the rule
for each of the following tables of values, find the rule and complete the table.
a) \\(y = \underline{\quad\quad}\\)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline x & 2 & 5 & 8 & 7 & 1 & 0 \\\\ \\hline y & 9 & 12 & 15 & 14 & 6 & 3 \\\\ \\hline \\end{array}$$

b) \\(y = \underline{\quad\quad}\\)
\

$$\begin{array}{|c|c|c|c|c|c|} \\hline x & 5 & 8 & 11 & 7 & 10 \\\\ \\hline y & 1 & 4 & 7 & 3 & 4 \\\\ \\hline \\end{array}$$

c) \\(y = \underline{\quad\quad}\\)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline x & 2 & 3 & 7 & 5 & 8 & 1 \\\\ \\hline y & 8 & 12 & 28 & 20 & & 4 \\\\ \\hline \\end{array}$$

d)
\

$$\begin{array}{|c|c|c|c|c|c|} \\hline h & 12 & 6 & 2 & 10 & 4 \\\\ \\hline t & 6 & 3 & 1 & 5 & 8 \\\\ \\hline \\end{array}$$

e)
\

$$\begin{array}{|c|c|c|c|c|c|} \\hline h & 6 & 9 & 2 & 4 & 12 \\\\ \\hline t & 14 & 17 & 10 & 12 & 7 \\\\ \\hline \\end{array}$$

f)
\

$$\begin{array}{|c|c|c|c|c|c|} \\hline h & 5 & 3 & 11 & 9 & 4 \\\\ \\hline t & 2 & 0 & 8 & 6 & 8 \\\\ \\hline \\end{array}$$

g)
\

$$\begin{array}{|c|c|c|c|c|c|} \\hline c & 3 & 8 & 5 & 1 & 10 \\\\ \\hline d & 18 & 48 & 30 & 6 & 6 \\\\ \\hline \\end{array}$$

h)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline c & 12 & 10 & 7 & 8 & 16 & 13 \\\\ \\hline d & 7 & 5 & 2 & 3 & & \\\\ \\hline \\end{array}$$

i)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline c & 3 & 7 & 1 & 12 & 9 & 6 \\\\ \\hline d & 13 & 17 & 11 & 22 & & \\\\ \\hline \\end{array}$$

j)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline k & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline p & 6 & 9 & 12 & 15 & & \\\\ \\hline \\end{array}$$

k)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline k & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline p & 9 & 10 & 11 & 12 & & \\\\ \\hline \\end{array}$$

l)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline k & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline p & 4 & 6 & 8 & 10 & & \\\\ \\hline \\end{array}$$

m)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline u & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline v & -1 & 2 & 5 & 8 & & \\\\ \\hline \\end{array}$$

n)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline u & 0 & 1 & 2 & 3 & 4 & 5 \\\\ \\hline v & 1 & 6 & 11 & 16 & & \\\\ \\hline \\end{array}$$

o)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline u & 4 & 5 & 6 & 7 & 8 & 9 \\\\ \\hline v & 4 & 6 & 8 & 10 & & \\\\ \\hline \\end{array}$$

p)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline s & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline z & 10 & 14 & 18 & 22 & & \\\\ \\hline \\end{array}$$

q)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline s & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline z & 6 & 9 & 12 & 15 & & \\\\ \\hline \\end{array}$$

r)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline s & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline z & 10 & 18 & 26 & 34 & & \\\\ \\hline \\end{array}$$

s)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline g & 3 & 4 & 5 & 6 & 7 & 8 \\\\ \\hline n & 7 & 8 & 9 & 10 & & \\\\ \\hline \\end{array}$$

t)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline g & 0 & 1 & 2 & 3 & 4 & 5 \\\\ \\hline n & 9 & 12 & 15 & 18 & & \\\\ \\hline \\end{array}$$

u)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline g & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline n & 7 & 14 & 21 & 28 & & \\\\ \\hline \\end{array}$$

v)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline i & 2 & 3 & 4 & 5 & 6 & 7 \\\\ \\hline m & 26 & 36 & 46 & 56 & & \\\\ \\hline \\end{array}$$

w)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline i & 1 & 2 & 3 & 4 & 5 & 6 \\\\ \\hline m & 1 & 7 & 13 & 19 & & \\\\ \\hline \\end{array}$$

x)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline i & 4 & 7 & 2 & 9 & 1 & 10 \\\\ \\hline m & 9 & 15 & 5 & 19 & & \\\\ \\hline \\end{array}$$

y)
\

$$\begin{array}{|c|c|c|c|c|c|c|} \\hline i & 2 & 7 & 11 & 8 & 4 & 5 \\\\ \\hline m & 1 & 16 & 28 & 19 & & \\\\ \\hline \\end{array}$$

Explanation:

Analyze the linear relationship for each table

For each sub-question, we find the linear rule of the form \(y = mx + c\) (or using the respective variables) by calculating the slope \(m = \frac{\Delta y}{\Delta x}\) and the constant \(c\). Then, we use the rule to fill in the missing value in the table.

  • a: Points \((2,5), (5,8)\). Slope \(m = \frac{8-5}{5-2} = 1\). Rule: \(y = x + 3\). Missing value for \(x=5\): \(y = 5+3 = 8\) (already filled as 8). Missing value for \(x=1\): \(y = 1+3 = 4\). Missing value for \(x=0\): \(y = 0+3 = 3\).
  • b: Points \((5,8), (8,11)\). Slope \(m = \frac{11-8}{8-5} = 1\). Rule: \(y = x + 3\). Missing value for \(x=1\): \(y = 1+3 = 4\). Missing value for \(x=10\): \(y = 10+3 = 13\).
  • c: Points \((2,8), (3,12)\). Slope \(m = \frac{12-8}{3-2} = 4\). Rule: \(y = 4x\). Missing value for \(x=5\): \(y = 4(5) = 20\). Missing value for \(x=1\): \(y = 4(1) = 4\).
  • d: Points \((12,6), (6,3)\). Slope \(m = \frac{3-6}{6-12} = 0.5\). Rule: \(t = 0.5h\). Missing value for \(h=10\): \(t = 5\). Missing value for \(h=4\): \(t = 2\).
  • e: Points \((6,14), (9,17)\). Slope \(m = \frac{17-14}{9-6} = 1\). Rule: \(t = h + 8\). Missing value for \(h=2\): \(t = 10\). Missing value for \(h=12\): \(t = 20\).
  • f: Points \((5,2), (3,0)\). Slope \(m = \frac{0-2}{3-5} = 1\). Rule: \(t = h - 3\). Missing value for \(h=11\): \(t = 8\). Missing value for \(h=9\): \(t = 6\).
  • g: Points \((3,18), (8,48)\). Slope \(m = \frac{48-18}{8-3} = 6\). Rule: \(d = 6c\). Missing value for \(c=5\): \(d = 30\). Missing value for \(c=10\): \(d = 60\).
  • h: Points \((12,7), (10,5)\). Slope \(m = \frac{5-7}{10-12} = 1\). Rule: \(d = c - 5\). Missing value for \(c=16\): \(d = 11\). Missing value for \(c=13\): \(d = 8\).
  • i: Points \((3,13), (7,17)\). Slope \(m = \frac{17-13}{7-3} = 1\). Rule: \(d = c + 10\). Missing value for \(c=12\): \(d = 22\). Missing value for \(c=9\): \(d = 19\).
  • j: Points \((2,6), (3,9)\). Slope \(m = \frac{9-6}{3-2} = 3\). Rule: \(p = 3k\). Missing value for \(k=6\): \(p = 18\). Missing value for \(k=7\): \(p = 21\).
  • k: Points \((1,9), (2,10)\). Slope \(m = \frac{10-9}{2-1} = 1\). Rule: \(p = k + 8\). Missing value for \(k=5\): \(p = 13\). Missing value for \(k=6\): \(p = 14\).
  • l: Points \((1,4), (2,6)\). Slope \(m = \frac{6-4}{2-1} = 2\). Rule: \(p = 2k + 2\). Missing value for \(k=5\): \(p = 12\). Missing value for \(k=6\): \(p = 14\).
  • m: Points \((1,-1), (2,2)\). Slope \(m = \frac{2 - (-1)}{2-1} = 3\). Rule: \(v = 3u - 4\). Missing value for \(u=5\): \(v = 11\). Missing value for \(u=6\): \(v = 14\).
  • n: Points \((0,1), (1,6)\). Slope \(m = \frac{6-1}{1-0} = 5\). Rule: \(v = 5u + 1\). Missing value for \(u=4\): \(v = 21\). Missing value for \(u=5\): \(v = 26\).
  • o: Points \((4,4), (5,6)\). Slope \(m = \frac{6-4}{5-4} = 2\). Rule: \(v = 2u - 4\). Missing value for \(u=8\): \(v = 12\). Missing value for \(u=9\): \(v = 14\).
  • p: Points \((2,10), (3,14)\). Slope \(m = \frac{14-10}{3-2} = 4\). Rule: \(z = 4s + 2\). Missing value for \(s=6\): \(z = 26\). Missing value for \(s=7\): \(z = 30\).
  • q: Points \((1,6),…

Answer:

No.RuleCompleted Values

ightarrow y=4\), \(x=0
ightarrow y=3\) |

b\(y = x + 3\)\(x=1

ightarrow y=4\), \(x=10
ightarrow y=13\) |

c\(y = 4x\)\(x=5

ightarrow y=20\), \(x=1
ightarrow y=4\) |

d\(t = 0.5h\)\(h=10

ightarrow t=5\), \(h=4
ightarrow t=2\) |

e\(t = h + 8\)\(h=2

ightarrow t=10\), \(h=12
ightarrow t=20\) |

f\(t = h - 3\)\(h=11

ightarrow t=8\), \(h=9
ightarrow t=6\) |

g\(d = 6c\)\(c=5

ightarrow d=30\), \(c=10
ightarrow d=60\) |

h\(d = c - 5\)\(c=16

ightarrow d=11\), \(c=13
ightarrow d=8\) |

i\(d = c + 10\)\(c=12

ightarrow d=22\), \(c=9
ightarrow d=19\) |

j\(p = 3k\)\(k=6

ightarrow p=18\), \(k=7
ightarrow p=21\) |

k\(p = k + 8\)\(k=5

ightarrow p=13\), \(k=6
ightarrow p=14\) |

l\(p = 2k + 2\)\(k=5

ightarrow p=12\), \(k=6
ightarrow p=14\) |

m\(v = 3u - 4\)\(u=5

ightarrow v=11\), \(u=6
ightarrow v=14\) |

n\(v = 5u + 1\)\(u=4

ightarrow v=21\), \(u=5
ightarrow v=26\) |

o\(v = 2u - 4\)\(u=8

ightarrow v=12\), \(u=9
ightarrow v=14\) |

p\(z = 4s + 2\)\(s=6

ightarrow z=26\), \(s=7
ightarrow z=30\) |

q\(z = 3s + 3\)\(s=5

ightarrow z=18\), \(s=6
ightarrow z=21\) |

r\(z = 8s + 2\)\(s=5

ightarrow z=42\), \(s=6
ightarrow z=50\) |

s\(n = g + 4\)\(g=7

ightarrow n=11\), \(g=8
ightarrow n=12\) |

t\(n = 3g + 9\)\(g=4

ightarrow n=21\), \(g=5
ightarrow n=24\) |

u\(n = 7g\)\(g=5

ightarrow n=35\), \(g=6
ightarrow n=42\) |

v\(m = 10i + 6\)\(i=6

ightarrow m=66\), \(i=7
ightarrow m=76\) |

w\(m = 6i - 5\)\(i=5

ightarrow m=25\), \(i=6
ightarrow m=31\) |

x\(m = 2i + 1\)\(i=1

ightarrow m=3\), \(i=10
ightarrow m=21\) |

y\(m = 3i - 5\)\(i=4

ightarrow m=7\), \(i=5
ightarrow m=10\) |