Graph Using a Table of Values 6y=2x-5

$6 y = 2 x - 5$

Step 1

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

$6 y = 2 (- 2) - 5$

Step 2

Solve the equation for $y$ .

Simplify.

Multiply $2$ by $- 2$ .

$6 y = - 4 - 5$

Subtract $5$ from $- 4$ .

$6 y = - 9$

Divide each term in $6 y = - 9$ by $6$ and simplify.

Divide each term in $6 y = - 9$ by $6$ .

$\frac{6 y}{6} = \frac{- 9}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 9}{6}$

Divide $y$ by $1$ .

$y = \frac{- 9}{6}$

Simplify the right side.

Cancel the common factor of $- 9$ and $6$ .

Factor $3$ out of $- 9$ .

$y = \frac{3 (- 3)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Move the negative in front of the fraction.

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

Step 3

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

$6 y = 2 (- 1) - 5$

Step 4

Solve the equation for $y$ .

Simplify.

Multiply $2$ by $- 1$ .

$6 y = - 2 - 5$

Subtract $5$ from $- 2$ .

$6 y = - 7$

Divide each term in $6 y = - 7$ by $6$ and simplify.

Divide each term in $6 y = - 7$ by $6$ .

$\frac{6 y}{6} = \frac{- 7}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 7}{6}$

Divide $y$ by $1$ .

$y = \frac{- 7}{6}$

Simplify the right side.

Move the negative in front of the fraction.

$y = - \frac{7}{6}$

Step 5

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

$6 y = 2 (0) - 5$

Step 6

Solve the equation for $y$ .

Simplify.

Multiply $2$ by $0$ .

$6 y = 0 - 5$

Subtract $5$ from $0$ .

$6 y = - 5$

Divide each term in $6 y = - 5$ by $6$ and simplify.

Divide each term in $6 y = - 5$ by $6$ .

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 7

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

$6 y = 2 (1) - 5$

Step 8

Solve the equation for $y$ .

Simplify.

Multiply $2$ by $1$ .

$6 y = 2 - 5$

Subtract $5$ from $2$ .

$6 y = - 3$

Divide each term in $6 y = - 3$ by $6$ and simplify.

Divide each term in $6 y = - 3$ by $6$ .

$\frac{6 y}{6} = \frac{- 3}{6}$

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

$\frac{6 y}{6} = \frac{- 3}{6}$

Divide $y$ by $1$ .

$y = \frac{- 3}{6}$

Simplify the right side.

Cancel the common factor of $- 3$ and $6$ .

Factor $3$ out of $- 3$ .

$y = \frac{3 (- 1)}{6}$

Cancel the common factors.

Factor $3$ out of $6$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = \frac{- 1}{2}$

Move the negative in front of the fraction.

$y = - \frac{1}{2}$

Step 9

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

$6 y = 2 (2) - 5$

Step 10

Solve the equation for $y$ .

Simplify.

Multiply $2$ by $2$ .

$6 y = 4 - 5$

Subtract $5$ from $4$ .

$6 y = - 1$

Divide each term in $6 y = - 1$ by $6$ and simplify.

Divide each term in $6 y = - 1$ by $6$ .

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

Simplify the left side.

Cancel the common factor of $6$ .

Cancel the common factor.

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

Divide $y$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 11

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

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

Step 12

Graph Using a Table of Values 6y=2x-5

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