Graph Using a Table of Values y+20=1/12(x+268)

$y + 20 = \frac{1}{12} (x + 268)$

Step 1

Substitute $- 2$ for $x$ and find the result for $y$ .

$y + 20 = \frac{1}{12} \cdot ((- 2) + 268)$

Step 2

Solve the equation for $y$ .

Simplify $\frac{1}{12} \cdot ((- 2) + 268)$ .

Rewrite.

$y + 20 = 0 + 0 + \frac{1}{12} \cdot ((- 2) + 268)$

Add $- 2$ and $268$ .

$y + 20 = \frac{1}{12} \cdot 266$

Cancel the common factor of $2$ .

Factor $2$ out of $12$ .

$y + 20 = \frac{1}{2 (6)} \cdot 266$

Factor $2$ out of $266$ .

$y + 20 = \frac{1}{2 \cdot 6} \cdot (2 \cdot 133)$

Cancel the common factor.

$y + 20 = \frac{1}{2 \cdot 6} \cdot (2 \cdot 133)$

Rewrite the expression.

$y + 20 = \frac{1}{6} \cdot 133$

Combine $\frac{1}{6}$ and $133$ .

$y + 20 = \frac{133}{6}$

Move all terms not containing $y$ to the right side of the equation.

Subtract $20$ from both sides of the equation.

$y = \frac{133}{6} - 20$

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = \frac{133}{6} - 20 \cdot \frac{6}{6}$

Combine $- 20$ and $\frac{6}{6}$ .

$y = \frac{133}{6} + \frac{- 20 \cdot 6}{6}$

Combine the numerators over the common denominator.

$y = \frac{133 - 20 \cdot 6}{6}$

Simplify the numerator.

Multiply $- 20$ by $6$ .

$y = \frac{133 - 120}{6}$

Subtract $120$ from $133$ .

$y = \frac{13}{6}$

Step 3

Substitute $- 1$ for $x$ and find the result for $y$ .

$y + 20 = \frac{1}{12} \cdot ((- 1) + 268)$

Step 4

Solve the equation for $y$ .

Simplify $\frac{1}{12} \cdot ((- 1) + 268)$ .

Rewrite.

$y + 20 = 0 + 0 + \frac{1}{12} \cdot ((- 1) + 268)$

Add $- 1$ and $268$ .

$y + 20 = \frac{1}{12} \cdot 267$

Cancel the common factor of $3$ .

Factor $3$ out of $12$ .

$y + 20 = \frac{1}{3 (4)} \cdot 267$

Factor $3$ out of $267$ .

$y + 20 = \frac{1}{3 \cdot 4} \cdot (3 \cdot 89)$

Cancel the common factor.

$y + 20 = \frac{1}{3 \cdot 4} \cdot (3 \cdot 89)$

Rewrite the expression.

$y + 20 = \frac{1}{4} \cdot 89$

Combine $\frac{1}{4}$ and $89$ .

$y + 20 = \frac{89}{4}$

Move all terms not containing $y$ to the right side of the equation.

Subtract $20$ from both sides of the equation.

$y = \frac{89}{4} - 20$

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$y = \frac{89}{4} - 20 \cdot \frac{4}{4}$

Combine $- 20$ and $\frac{4}{4}$ .

$y = \frac{89}{4} + \frac{- 20 \cdot 4}{4}$

Combine the numerators over the common denominator.

$y = \frac{89 - 20 \cdot 4}{4}$

Simplify the numerator.

Multiply $- 20$ by $4$ .

$y = \frac{89 - 80}{4}$

Subtract $80$ from $89$ .

$y = \frac{9}{4}$

Step 5

Substitute $0$ for $x$ and find the result for $y$ .

$y + 20 = \frac{1}{12} \cdot ((0) + 268)$

Step 6

Solve the equation for $y$ .

Simplify $\frac{1}{12} \cdot ((0) + 268)$ .

Add $0$ and $268$ .

$y + 20 = \frac{1}{12} \cdot 268$

Cancel the common factor of $4$ .

Factor $4$ out of $12$ .

$y + 20 = \frac{1}{4 (3)} \cdot 268$

Factor $4$ out of $268$ .

$y + 20 = \frac{1}{4 \cdot 3} \cdot (4 \cdot 67)$

Cancel the common factor.

$y + 20 = \frac{1}{4 \cdot 3} \cdot (4 \cdot 67)$

Rewrite the expression.

$y + 20 = \frac{1}{3} \cdot 67$

Combine $\frac{1}{3}$ and $67$ .

$y + 20 = \frac{67}{3}$

Move all terms not containing $y$ to the right side of the equation.

Subtract $20$ from both sides of the equation.

$y = \frac{67}{3} - 20$

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{67}{3} - 20 \cdot \frac{3}{3}$

Combine $- 20$ and $\frac{3}{3}$ .

$y = \frac{67}{3} + \frac{- 20 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{67 - 20 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 20$ by $3$ .

$y = \frac{67 - 60}{3}$

Subtract $60$ from $67$ .

$y = \frac{7}{3}$

Step 7

Substitute $1$ for $x$ and find the result for $y$ .

$y + 20 = \frac{1}{12} \cdot ((1) + 268)$

Step 8

Solve the equation for $y$ .

Simplify $\frac{1}{12} \cdot ((1) + 268)$ .

Rewrite.

$y + 20 = 0 + 0 + \frac{1}{12} \cdot ((1) + 268)$

Add $1$ and $268$ .

$y + 20 = \frac{1}{12} \cdot 269$

Combine $\frac{1}{12}$ and $269$ .

$y + 20 = \frac{269}{12}$

Move all terms not containing $y$ to the right side of the equation.

Subtract $20$ from both sides of the equation.

$y = \frac{269}{12} - 20$

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{12}{12}$ .

$y = \frac{269}{12} - 20 \cdot \frac{12}{12}$

Combine $- 20$ and $\frac{12}{12}$ .

$y = \frac{269}{12} + \frac{- 20 \cdot 12}{12}$

Combine the numerators over the common denominator.

$y = \frac{269 - 20 \cdot 12}{12}$

Simplify the numerator.

Multiply $- 20$ by $12$ .

$y = \frac{269 - 240}{12}$

Subtract $240$ from $269$ .

$y = \frac{29}{12}$

Step 9

Substitute $2$ for $x$ and find the result for $y$ .

$y + 20 = \frac{1}{12} \cdot ((2) + 268)$

Step 10

Solve the equation for $y$ .

Simplify $\frac{1}{12} \cdot ((2) + 268)$ .

Rewrite.

$y + 20 = 0 + 0 + \frac{1}{12} \cdot ((2) + 268)$

Add $2$ and $268$ .

$y + 20 = \frac{1}{12} \cdot 270$

Cancel the common factor of $6$ .

Factor $6$ out of $12$ .

$y + 20 = \frac{1}{6 (2)} \cdot 270$

Factor $6$ out of $270$ .

$y + 20 = \frac{1}{6 \cdot 2} \cdot (6 \cdot 45)$

Cancel the common factor.

$y + 20 = \frac{1}{6 \cdot 2} \cdot (6 \cdot 45)$

Rewrite the expression.

$y + 20 = \frac{1}{2} \cdot 45$

Combine $\frac{1}{2}$ and $45$ .

$y + 20 = \frac{45}{2}$

Move all terms not containing $y$ to the right side of the equation.

Subtract $20$ from both sides of the equation.

$y = \frac{45}{2} - 20$

To write $- 20$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$y = \frac{45}{2} - 20 \cdot \frac{2}{2}$

Combine $- 20$ and $\frac{2}{2}$ .

$y = \frac{45}{2} + \frac{- 20 \cdot 2}{2}$

Combine the numerators over the common denominator.

$y = \frac{45 - 20 \cdot 2}{2}$

Simplify the numerator.

Multiply $- 20$ by $2$ .

$y = \frac{45 - 40}{2}$

Subtract $40$ from $45$ .

$y = \frac{5}{2}$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & \frac{13}{6} \\ - 1 & \frac{9}{4} \\ 0 & \frac{7}{3} \\ 1 & \frac{29}{12} \\ 2 & \frac{5}{2} \end{array}$

Step 12

Graph Using a Table of Values y+20=1/12(x+268)

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