Graph Using a Table of Values 2x+5y=16

$2 x + 5 y = 16$

Step 1

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

$2 (- 2) + 5 y = 16$

Step 2

Solve the equation for $y$ .

Multiply $2$ by $- 2$ .

$- 4 + 5 y = 16$

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

Add $4$ to both sides of the equation.

$5 y = 16 + 4$

Add $16$ and $4$ .

$5 y = 20$

Divide each term in $5 y = 20$ by $5$ and simplify.

Divide each term in $5 y = 20$ by $5$ .

$\frac{5 y}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{20}{5}$

Divide $y$ by $1$ .

$y = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$y = 4$

Step 3

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

$2 (- 1) + 5 y = 16$

Step 4

Solve the equation for $y$ .

Multiply $2$ by $- 1$ .

$- 2 + 5 y = 16$

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

Add $2$ to both sides of the equation.

$5 y = 16 + 2$

Add $16$ and $2$ .

$5 y = 18$

Divide each term in $5 y = 18$ by $5$ and simplify.

Divide each term in $5 y = 18$ by $5$ .

$\frac{5 y}{5} = \frac{18}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{18}{5}$

Divide $y$ by $1$ .

$y = \frac{18}{5}$

Step 5

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

$2 (0) + 5 y = 16$

Step 6

Solve the equation for $y$ .

Simplify $2 (0) + 5 y$ .

Multiply $2$ by $0$ .

$0 + 5 y = 16$

Add $0$ and $5 y$ .

$5 y = 16$

Divide each term in $5 y = 16$ by $5$ and simplify.

Divide each term in $5 y = 16$ by $5$ .

$\frac{5 y}{5} = \frac{16}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{16}{5}$

Divide $y$ by $1$ .

$y = \frac{16}{5}$

Step 7

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

$2 (1) + 5 y = 16$

Step 8

Solve the equation for $y$ .

Multiply $2$ by $1$ .

$2 + 5 y = 16$

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

Subtract $2$ from both sides of the equation.

$5 y = 16 - 2$

Subtract $2$ from $16$ .

$5 y = 14$

Divide each term in $5 y = 14$ by $5$ and simplify.

Divide each term in $5 y = 14$ by $5$ .

$\frac{5 y}{5} = \frac{14}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{14}{5}$

Divide $y$ by $1$ .

$y = \frac{14}{5}$

Step 9

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

$2 (2) + 5 y = 16$

Step 10

Solve the equation for $y$ .

Multiply $2$ by $2$ .

$4 + 5 y = 16$

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

Subtract $4$ from both sides of the equation.

$5 y = 16 - 4$

Subtract $4$ from $16$ .

$5 y = 12$

Divide each term in $5 y = 12$ by $5$ and simplify.

Divide each term in $5 y = 12$ by $5$ .

$\frac{5 y}{5} = \frac{12}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 y}{5} = \frac{12}{5}$

Divide $y$ by $1$ .

$y = \frac{12}{5}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & 4 \\ - 1 & \frac{18}{5} \\ 0 & \frac{16}{5} \\ 1 & \frac{14}{5} \\ 2 & \frac{12}{5} \end{array}$

Step 12

Graph Using a Table of Values 2x+5y=16

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