Question

write an equation to represent each function
1.
input ( x ) | 0 | 1 | 2 | 3 | 4
output ( y ) | 0 | 9 | 18 | 27 | 36

2.
input ( x ) | 1 | 2 | 3 | 4 | 5
output ( y ) | 2 | 4 | 6 | 8 | 10

3.
input ( x ) | 1 | 2 | 3 | 4 | 5
output ( y ) | 7 | 14 | 21 | 28 | 35

4.
input ( x ) | 0 | 1 | 2 | 3 | 4
output ( y ) | 0 | 4 | 8 | 12 | 16

write an equation to represent each function.
1.
input ( x ) | 3 | 4 | 5 | 6
output ( y ) | 10 | 12 | 14 | 16

2.
input ( x ) | 0 | 1 | 2 | 3
output ( y ) | 2 | 6 | 10 | 14

3.
input ( x ) | 5 | 6 | 7 | 8
output ( y ) | 14 | 17 | 20 | 23

4.
input ( x ) | 6 | 7 | 8 | 9
output ( y ) | 12 | 19 | 26 | 33

5.
input ( x ) | 0 | 1 | 2 | 3
output ( y ) | 17 | 19 | 21 | 23

6.
input ( x ) | 0 | 1 | 2 | 3 | 4
output ( y ) | 2 | 14 | 26 | 38 | 50

Explanation:

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Top Section (Problems 1-4)

Problem 1

Step1: Find ratio of y to x

$\frac{y}{x} = \frac{0}{0}=0, \frac{9}{1}=9, \frac{18}{2}=9, \frac{27}{3}=9, \frac{36}{4}=9$

Step2: Define linear relationship

$y = 9x$

Problem 2

Step1: Find ratio of y to x

$\frac{y}{x} = \frac{2}{1}=2, \frac{4}{2}=2, \frac{6}{3}=2, \frac{8}{4}=2, \frac{10}{5}=2$

Step2: Define linear relationship

$y = 2x$

Problem 3

Step1: Find ratio of y to x

$\frac{y}{x} = \frac{7}{1}=7, \frac{14}{2}=7, \frac{21}{3}=7, \frac{28}{4}=7, \frac{35}{5}=7$

Step2: Define linear relationship

$y = 7x$

Problem 4

Step1: Find ratio of y to x

$\frac{y}{x} = \frac{0}{0}=0, \frac{4}{1}=4, \frac{8}{2}=4, \frac{12}{3}=4, \frac{16}{4}=4$

Step2: Define linear relationship

$y = 4x$
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Bottom Section (Problems 1-6)

Problem 1

Step1: Calculate slope (m)

$m = \frac{12-10}{4-3} = 2$

Step2: Find y-intercept (b)

$10 = 2(3) + b \implies b=4$

Step3: Write linear equation

$y = 2x + 4$

Problem 2

Step1: Calculate slope (m)

$m = \frac{6-2}{1-0} = 4$

Step2: Find y-intercept (b)

$b = 2$ (when $x=0$)

Step3: Write linear equation

$y = 4x + 2$

Problem 3

Step1: Calculate slope (m)

$m = \frac{17-14}{6-5} = 3$

Step2: Find y-intercept (b)

$14 = 3(5) + b \implies b=-1$

Step3: Write linear equation

$y = 3x - 1$

Problem 4

Step1: Calculate slope (m)

$m = \frac{19-12}{7-6} = 7$

Step2: Find y-intercept (b)

$12 = 7(6) + b \implies b=-30$

Step3: Write linear equation

$y = 7x - 30$

Problem 5

Step1: Calculate slope (m)

$m = \frac{19-17}{1-0} = 2$

Step2: Find y-intercept (b)

$b = 17$ (when $x=0$)

Step3: Write linear equation

$y = 2x + 17$

Problem 6

Step1: Calculate slope (m)

$m = \frac{14-2}{1-0} = 12$

Step2: Find y-intercept (b)

$b = 2$ (when $x=0$)

Step3: Write linear equation

$y = 12x + 2$
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Answer:

Top Section

1. $y = 9x$
2. $y = 2x$
3. $y = 7x$
4. $y = 4x$

Bottom Section

1. $y = 2x + 4$
2. $y = 4x + 2$
3. $y = 3x - 1$
4. $y = 7x - 30$
5. $y = 2x + 17$
6. $y = 12x + 2$