Graph Using a Table of Values 5x+10y=15

$5 x + 10 y = 15$

Step 1

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

$5 (- 2) + 10 y = 15$

Step 2

Solve the equation for $y$ .

Multiply $5$ by $- 2$ .

$- 10 + 10 y = 15$

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

Add $10$ to both sides of the equation.

$10 y = 15 + 10$

Add $15$ and $10$ .

$10 y = 25$

Divide each term in $10 y = 25$ by $10$ and simplify.

Divide each term in $10 y = 25$ by $10$ .

$\frac{10 y}{10} = \frac{25}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{25}{10}$

Divide $y$ by $1$ .

$y = \frac{25}{10}$

Simplify the right side.

Cancel the common factor of $25$ and $10$ .

Factor $5$ out of $25$ .

$y = \frac{5 (5)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

$y = \frac{5 \cdot 5}{5 \cdot 2}$

Cancel the common factor.

$y = \frac{5 \cdot 5}{5 \cdot 2}$

Rewrite the expression.

$y = \frac{5}{2}$

Step 3

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

$5 (- 1) + 10 y = 15$

Step 4

Solve the equation for $y$ .

Multiply $5$ by $- 1$ .

$- 5 + 10 y = 15$

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

Add $5$ to both sides of the equation.

$10 y = 15 + 5$

Add $15$ and $5$ .

$10 y = 20$

Divide each term in $10 y = 20$ by $10$ and simplify.

Divide each term in $10 y = 20$ by $10$ .

$\frac{10 y}{10} = \frac{20}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{20}{10}$

Divide $y$ by $1$ .

$y = \frac{20}{10}$

Simplify the right side.

Divide $20$ by $10$ .

$y = 2$

Step 5

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

$5 (0) + 10 y = 15$

Step 6

Solve the equation for $y$ .

Simplify $5 (0) + 10 y$ .

Multiply $5$ by $0$ .

$0 + 10 y = 15$

Add $0$ and $10 y$ .

$10 y = 15$

Divide each term in $10 y = 15$ by $10$ and simplify.

Divide each term in $10 y = 15$ by $10$ .

$\frac{10 y}{10} = \frac{15}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{15}{10}$

Divide $y$ by $1$ .

$y = \frac{15}{10}$

Simplify the right side.

Cancel the common factor of $15$ and $10$ .

Factor $5$ out of $15$ .

$y = \frac{5 (3)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 7

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

$5 (1) + 10 y = 15$

Step 8

Solve the equation for $y$ .

Multiply $5$ by $1$ .

$5 + 10 y = 15$

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

Subtract $5$ from both sides of the equation.

$10 y = 15 - 5$

Subtract $5$ from $15$ .

$10 y = 10$

Divide each term in $10 y = 10$ by $10$ and simplify.

Divide each term in $10 y = 10$ by $10$ .

$\frac{10 y}{10} = \frac{10}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{10}{10}$

Divide $y$ by $1$ .

$y = \frac{10}{10}$

Simplify the right side.

Divide $10$ by $10$ .

$y = 1$

Step 9

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

$5 (2) + 10 y = 15$

Step 10

Solve the equation for $y$ .

Multiply $5$ by $2$ .

$10 + 10 y = 15$

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

Subtract $10$ from both sides of the equation.

$10 y = 15 - 10$

Subtract $10$ from $15$ .

$10 y = 5$

Divide each term in $10 y = 5$ by $10$ and simplify.

Divide each term in $10 y = 5$ by $10$ .

$\frac{10 y}{10} = \frac{5}{10}$

Simplify the left side.

Cancel the common factor of $10$ .

Cancel the common factor.

$\frac{10 y}{10} = \frac{5}{10}$

Divide $y$ by $1$ .

$y = \frac{5}{10}$

Simplify the right side.

Cancel the common factor of $5$ and $10$ .

Factor $5$ out of $5$ .

$y = \frac{5 (1)}{10}$

Cancel the common factors.

Factor $5$ out of $10$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Step 11

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

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

Step 12

Graph Using a Table of Values 5x+10y=15

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