Graph Using a Table of Values y=5/6x-1

$y = \frac{5}{6} x - 1$

Step 1

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

$y = \frac{5}{6} \cdot (- 2) - 1$

Step 2

Solve the equation for $y$ .

Multiply $\frac{5}{6}$ by $- 2$ .

$y = \frac{5}{6} \cdot - 2 - 1$

Simplify $\frac{5}{6} \cdot - 2 - 1$ .

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$y = \frac{5}{2 (3)} \cdot - 2 - 1$

Factor $2$ out of $- 2$ .

$y = \frac{5}{2 \cdot 3} \cdot (2 \cdot - 1) - 1$

Cancel the common factor.

$y = \frac{5}{2 \cdot 3} \cdot (2 \cdot - 1) - 1$

Rewrite the expression.

$y = \frac{5}{3} \cdot - 1 - 1$

Combine $\frac{5}{3}$ and $- 1$ .

$y = \frac{5 \cdot - 1}{3} - 1$

Multiply $5$ by $- 1$ .

$y = \frac{- 5}{3} - 1$

Move the negative in front of the fraction.

$y = - \frac{5}{3} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = - \frac{5}{3} - 1 \cdot \frac{3}{3}$

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

$y = - \frac{5}{3} + \frac{- 1 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 5 - 1 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$y = \frac{- 5 - 3}{3}$

Subtract $3$ from $- 5$ .

$y = \frac{- 8}{3}$

Move the negative in front of the fraction.

$y = - \frac{8}{3}$

Step 3

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

$y = \frac{5}{6} \cdot (- 1) - 1$

Step 4

Solve the equation for $y$ .

Multiply $\frac{5}{6}$ by $- 1$ .

$y = \frac{5}{6} \cdot - 1 - 1$

Simplify $\frac{5}{6} \cdot - 1 - 1$ .

Simplify each term.

Multiply $\frac{5}{6} \cdot - 1$ .

Combine $\frac{5}{6}$ and $- 1$ .

$y = \frac{5 \cdot - 1}{6} - 1$

Multiply $5$ by $- 1$ .

$y = \frac{- 5}{6} - 1$

Move the negative in front of the fraction.

$y = - \frac{5}{6} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = - \frac{5}{6} - 1 \cdot \frac{6}{6}$

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

$y = - \frac{5}{6} + \frac{- 1 \cdot 6}{6}$

Combine the numerators over the common denominator.

$y = \frac{- 5 - 1 \cdot 6}{6}$

Simplify the numerator.

Multiply $- 1$ by $6$ .

$y = \frac{- 5 - 6}{6}$

Subtract $6$ from $- 5$ .

$y = \frac{- 11}{6}$

Move the negative in front of the fraction.

$y = - \frac{11}{6}$

Step 5

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

$y = \frac{5}{6} \cdot (0) - 1$

Step 6

Solve the equation for $y$ .

Multiply $\frac{5}{6}$ by $0$ .

$y = \frac{5}{6} \cdot 0 - 1$

Remove parentheses.

$y = \frac{5}{6} \cdot (0) - 1$

Simplify $\frac{5}{6} \cdot (0) - 1$ .

Multiply $\frac{5}{6}$ by $0$ .

$y = 0 - 1$

Subtract $1$ from $0$ .

$y = - 1$

Step 7

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

$y = \frac{5}{6} \cdot (1) - 1$

Step 8

Solve the equation for $y$ .

Multiply $\frac{5}{6}$ by $1$ .

$y = \frac{5}{6} \cdot 1 - 1$

Remove parentheses.

$y = \frac{5}{6} \cdot (1) - 1$

Simplify $\frac{5}{6} \cdot (1) - 1$ .

Multiply $\frac{5}{6}$ by $1$ .

$y = \frac{5}{6} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$y = \frac{5}{6} - 1 \cdot \frac{6}{6}$

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

$y = \frac{5}{6} + \frac{- 1 \cdot 6}{6}$

Combine the numerators over the common denominator.

$y = \frac{5 - 1 \cdot 6}{6}$

Simplify the numerator.

Multiply $- 1$ by $6$ .

$y = \frac{5 - 6}{6}$

Subtract $6$ from $5$ .

$y = \frac{- 1}{6}$

Move the negative in front of the fraction.

$y = - \frac{1}{6}$

Step 9

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

$y = \frac{5}{6} \cdot (2) - 1$

Step 10

Solve the equation for $y$ .

Multiply $\frac{5}{6}$ by $2$ .

$y = \frac{5}{6} \cdot 2 - 1$

Remove parentheses.

$y = \frac{5}{6} \cdot (2) - 1$

Simplify $\frac{5}{6} \cdot (2) - 1$ .

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$y = \frac{5}{2 (3)} \cdot 2 - 1$

Cancel the common factor.

$y = \frac{5}{2 \cdot 3} \cdot 2 - 1$

Rewrite the expression.

$y = \frac{5}{3} - 1$

To write $- 1$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = \frac{5}{3} - 1 \cdot \frac{3}{3}$

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

$y = \frac{5}{3} + \frac{- 1 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{5 - 1 \cdot 3}{3}$

Simplify the numerator.

Multiply $- 1$ by $3$ .

$y = \frac{5 - 3}{3}$

Subtract $3$ from $5$ .

$y = \frac{2}{3}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & - \frac{8}{3} \\ - 1 & - \frac{11}{6} \\ 0 & - 1 \\ 1 & - \frac{1}{6} \\ 2 & \frac{2}{3} \end{array}$

Step 12

Graph Using a Table of Values y=5/6x-1

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