Algebra Examples

$2 x + 4 y = 6 x - y$

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

Move all terms containing $y$ to the left side of the equation.

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Step 1.2.1

Add $y$ to both sides of the equation.

$2 x + 4 y + y = 6 x$

Step 1.2.2

Add $4 y$ and $y$ .

$2 x + 5 y = 6 x$

Step 1.3

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

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Step 1.3.1

Subtract $2 x$ from both sides of the equation.

$5 y = 6 x - 2 x$

Step 1.3.2

Subtract $2 x$ from $6 x$ .

$5 y = 4 x$

Step 1.4

Divide each term in $5 y = 4 x$ by $5$ and simplify.

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Step 1.4.1

Divide each term in $5 y = 4 x$ by $5$ .

$\frac{5 y}{5} = \frac{4 x}{5}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $5$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{4 x}{5}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{5}$

Step 1.5

Reorder terms.

$y = \frac{4}{5} x$

Step 2

Using the slope-intercept form, the slope is $\frac{4}{5}$ .

$m = \frac{4}{5}$

Step 3