Graph Using a Table of Values 7x+8y=56

$7 x + 8 y = 56$

Step 1

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

$7 (- 2) + 8 y = 56$

Step 2

Solve the equation for $y$ .

Multiply $7$ by $- 2$ .

$- 14 + 8 y = 56$

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

Add $14$ to both sides of the equation.

$8 y = 56 + 14$

Add $56$ and $14$ .

$8 y = 70$

Divide each term in $8 y = 70$ by $8$ and simplify.

Divide each term in $8 y = 70$ by $8$ .

$\frac{8 y}{8} = \frac{70}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{70}{8}$

Divide $y$ by $1$ .

$y = \frac{70}{8}$

Simplify the right side.

Cancel the common factor of $70$ and $8$ .

Factor $2$ out of $70$ .

$y = \frac{2 (35)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$y = \frac{2 \cdot 35}{2 \cdot 4}$

Cancel the common factor.

$y = \frac{2 \cdot 35}{2 \cdot 4}$

Rewrite the expression.

$y = \frac{35}{4}$

Step 3

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

$7 (- 1) + 8 y = 56$

Step 4

Solve the equation for $y$ .

Multiply $7$ by $- 1$ .

$- 7 + 8 y = 56$

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

Add $7$ to both sides of the equation.

$8 y = 56 + 7$

Add $56$ and $7$ .

$8 y = 63$

Divide each term in $8 y = 63$ by $8$ and simplify.

Divide each term in $8 y = 63$ by $8$ .

$\frac{8 y}{8} = \frac{63}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{63}{8}$

Divide $y$ by $1$ .

$y = \frac{63}{8}$

Step 5

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

$7 (0) + 8 y = 56$

Step 6

Solve the equation for $y$ .

Simplify $7 (0) + 8 y$ .

Multiply $7$ by $0$ .

$0 + 8 y = 56$

Add $0$ and $8 y$ .

$8 y = 56$

Divide each term in $8 y = 56$ by $8$ and simplify.

Divide each term in $8 y = 56$ by $8$ .

$\frac{8 y}{8} = \frac{56}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{56}{8}$

Divide $y$ by $1$ .

$y = \frac{56}{8}$

Simplify the right side.

Divide $56$ by $8$ .

$y = 7$

Step 7

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

$7 (1) + 8 y = 56$

Step 8

Solve the equation for $y$ .

Multiply $7$ by $1$ .

$7 + 8 y = 56$

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

Subtract $7$ from both sides of the equation.

$8 y = 56 - 7$

Subtract $7$ from $56$ .

$8 y = 49$

Divide each term in $8 y = 49$ by $8$ and simplify.

Divide each term in $8 y = 49$ by $8$ .

$\frac{8 y}{8} = \frac{49}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{49}{8}$

Divide $y$ by $1$ .

$y = \frac{49}{8}$

Step 9

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

$7 (2) + 8 y = 56$

Step 10

Solve the equation for $y$ .

Multiply $7$ by $2$ .

$14 + 8 y = 56$

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

Subtract $14$ from both sides of the equation.

$8 y = 56 - 14$

Subtract $14$ from $56$ .

$8 y = 42$

Divide each term in $8 y = 42$ by $8$ and simplify.

Divide each term in $8 y = 42$ by $8$ .

$\frac{8 y}{8} = \frac{42}{8}$

Simplify the left side.

Cancel the common factor of $8$ .

Cancel the common factor.

$\frac{8 y}{8} = \frac{42}{8}$

Divide $y$ by $1$ .

$y = \frac{42}{8}$

Simplify the right side.

Cancel the common factor of $42$ and $8$ .

Factor $2$ out of $42$ .

$y = \frac{2 (21)}{8}$

Cancel the common factors.

Factor $2$ out of $8$ .

$y = \frac{2 \cdot 21}{2 \cdot 4}$

Cancel the common factor.

$y = \frac{2 \cdot 21}{2 \cdot 4}$

Rewrite the expression.

$y = \frac{21}{4}$

Step 11

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

$\begin{array}{c} x & y \\ - 2 & \frac{35}{4} \\ - 1 & \frac{63}{8} \\ 0 & 7 \\ 1 & \frac{49}{8} \\ 2 & \frac{21}{4} \end{array}$

Step 12

Graph Using a Table of Values 7x+8y=56

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