Pre-Algebra Examples

$5 x = 4 x - y$

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

Rewrite the equation as $4 x - y = 5 x$ .

$4 x - y = 5 x$

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 $4 x$ from both sides of the equation.

$- y = 5 x - 4 x$

Step 1.3.2

Subtract $4 x$ from $5 x$ .

$- y = x$

Step 1.4

Divide each term in $- y = x$ by $- 1$ and simplify.

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Step 1.4.1

Divide each term in $- y = x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{x}{- 1}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{x}{- 1}$

Step 1.4.2.2

Divide $y$ by $1$ .

$y = \frac{x}{- 1}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y = - 1 \cdot x$

Step 1.4.3.2

Rewrite $- 1 \cdot x$ as $- x$ .

$y = - x$

Step 2

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

$m = - 1$

Step 3