Algebra Examples

$\frac{x + y}{3} + 3 = 17$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Step 1.2

Simplify the left side.

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Step 1.2.1

Simplify $\frac{x + y}{3} + 3$ .

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Step 1.2.1.1

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

$\frac{x + y}{3} + 3 \cdot \frac{3}{3} = 17$

Step 1.2.1.2

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

$\frac{x + y}{3} + \frac{3 \cdot 3}{3} = 17$

Step 1.2.1.3

Combine the numerators over the common denominator.

$\frac{x + y + 3 \cdot 3}{3} = 17$

Step 1.2.1.4

Multiply $3$ by $3$ .

$\frac{x + y + 9}{3} = 17$

Step 1.3

Multiply both sides of the equation by $3$ .

$3 \frac{x + y + 9}{3} = 3 \cdot 17$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $3$ .

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Step 1.4.1.1.1

Cancel the common factor.

$3 \frac{x + y + 9}{3} = 3 \cdot 17$

Step 1.4.1.1.2

Rewrite the expression.

$x + y + 9 = 3 \cdot 17$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Multiply $3$ by $17$ .

$x + y + 9 = 51$

Step 1.5

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

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Step 1.5.1

Subtract $x$ from both sides of the equation.

$y + 9 = 51 - x$

Step 1.5.2

Subtract $9$ from both sides of the equation.

$y = 51 - x - 9$

Step 1.5.3

Subtract $9$ from $51$ .

$y = - x + 42$

Step 2

Using the slope-intercept form, the slope is $- 1$ .

$m = - 1$

Step 3