Graph Using a Table of Values y=2/3x+3

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

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

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

Solve the equation for $y$ .

Multiply $\frac{2}{3}$ by $- 2$ .

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

Simplify $\frac{2}{3} \cdot - 2 + 3$ .

Simplify each term.

Multiply $\frac{2}{3} \cdot - 2$ .

Combine $\frac{2}{3}$ and $- 2$ .

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

Multiply $2$ by $- 2$ .

$y = \frac{- 4}{3} + 3$

Move the negative in front of the fraction.

$y = - \frac{4}{3} + 3$

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

$y = - \frac{4}{3} + 3 \cdot \frac{3}{3}$

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

$y = - \frac{4}{3} + \frac{3 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{- 4 + 3 \cdot 3}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$y = \frac{- 4 + 9}{3}$

Add $- 4$ and $9$ .

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

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

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

Solve the equation for $y$ .

Multiply $\frac{2}{3}$ by $- 1$ .

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

Simplify $\frac{2}{3} \cdot - 1 + 3$ .

Simplify each term.

Multiply $\frac{2}{3} \cdot - 1$ .

Combine $\frac{2}{3}$ and $- 1$ .

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

Multiply $2$ by $- 1$ .

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

Move the negative in front of the fraction.

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $3$ .

$y = \frac{- 2 + 9}{3}$

Add $- 2$ and $9$ .

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

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

$y = \frac{2}{3} \cdot (0) + 3$

Solve the equation for $y$ .

Multiply $\frac{2}{3}$ by $0$ .

$y = \frac{2}{3} \cdot 0 + 3$

Remove parentheses.

$y = \frac{2}{3} \cdot (0) + 3$

Simplify $\frac{2}{3} \cdot (0) + 3$ .

Multiply $\frac{2}{3}$ by $0$ .

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

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

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

Solve the equation for $y$ .

Multiply $\frac{2}{3}$ by $1$ .

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

Remove parentheses.

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

Simplify $\frac{2}{3} \cdot (1) + 3$ .

Multiply $\frac{2}{3}$ by $1$ .

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

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

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $3$ .

$y = \frac{2 + 9}{3}$

Add $2$ and $9$ .

$y = \frac{11}{3}$

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

$y = \frac{2}{3} \cdot (2) + 3$

Solve the equation for $y$ .

Multiply $\frac{2}{3}$ by $2$ .

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

Remove parentheses.

$y = \frac{2}{3} \cdot (2) + 3$

Simplify $\frac{2}{3} \cdot (2) + 3$ .

Multiply $\frac{2}{3} (2)$ .

Combine $\frac{2}{3}$ and $2$ .

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

Multiply $2$ by $2$ .

$y = \frac{4}{3} + 3$

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

$y = \frac{4}{3} + 3 \cdot \frac{3}{3}$

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

$y = \frac{4}{3} + \frac{3 \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = \frac{4 + 3 \cdot 3}{3}$

Simplify the numerator.

Multiply $3$ by $3$ .

$y = \frac{4 + 9}{3}$

Add $4$ and $9$ .

$y = \frac{13}{3}$

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

$\begin{array}{c} x & y \\ - 2 & \frac{5}{3} \\ - 1 & \frac{7}{3} \\ 0 & 3 \\ 1 & \frac{11}{3} \\ 2 & \frac{13}{3} \end{array}$

Graph Using a Table of Values y=2/3x+3

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