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

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

Step 1

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

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

Step 2

Solve the equation for $y$ .

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

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

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

Simplify each term.

Cancel the common factor of $2$ .

Factor $2$ out of $- 2$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = 3 \cdot - 1 + 3$

Multiply $3$ by $- 1$ .

$y = - 3 + 3$

Add $- 3$ and $3$ .

$y = 0$

Step 3

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

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

Step 4

Solve the equation for $y$ .

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

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

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

Simplify each term.

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

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

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

Multiply $3$ by $- 1$ .

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

Move the negative in front of the fraction.

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

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{- 3 + 6}{2}$

Add $- 3$ and $6$ .

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

Step 5

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

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

Step 6

Solve the equation for $y$ .

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

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

Remove parentheses.

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

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

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

$y = 0 + 3$

Add $0$ and $3$ .

$y = 3$

Step 7

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

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

Step 8

Solve the equation for $y$ .

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

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

Remove parentheses.

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

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

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

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

To write $3$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $3$ by $2$ .

$y = \frac{3 + 6}{2}$

Add $3$ and $6$ .

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

Step 9

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

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

Step 10

Solve the equation for $y$ .

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

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

Remove parentheses.

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

$y = 3 + 3$

Add $3$ and $3$ .

$y = 6$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 0 \\ - 1 & \frac{3}{2} \\ 0 & 3 \\ 1 & \frac{9}{2} \\ 2 & 6 \end{array}$

Step 12

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

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