Algebra Examples

$5 = 10 x - 5 y$

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 $10 x - 5 y = 5$ .

$10 x - 5 y = 5$

Step 1.3

Subtract $10 x$ from both sides of the equation.

$- 5 y = 5 - 10 x$

Step 1.4

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

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Step 1.4.1

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

$\frac{- 5 y}{- 5} = \frac{5}{- 5} + \frac{- 10 x}{- 5}$

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.

$\frac{- 5 y}{- 5} = \frac{5}{- 5} + \frac{- 10 x}{- 5}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{5}{- 5} + \frac{- 10 x}{- 5}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Simplify each term.

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Step 1.4.3.1.1

Divide $5$ by $- 5$ .

$y = - 1 + \frac{- 10 x}{- 5}$

Step 1.4.3.1.2

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

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Step 1.4.3.1.2.1

Factor $- 5$ out of $- 10 x$ .

$y = - 1 + \frac{- 5 (2 x)}{- 5}$

Step 1.4.3.1.2.2

Cancel the common factors.

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Step 1.4.3.1.2.2.1

Factor $- 5$ out of $- 5$ .

$y = - 1 + \frac{- 5 (2 x)}{- 5 (1)}$

Step 1.4.3.1.2.2.2

Cancel the common factor.

$y = - 1 + \frac{- 5 (2 x)}{- 5 \cdot 1}$

Step 1.4.3.1.2.2.3

Rewrite the expression.

$y = - 1 + \frac{2 x}{1}$

Step 1.4.3.1.2.2.4

Divide $2 x$ by $1$ .

$y = - 1 + 2 x$

Step 1.5

Reorder $- 1$ and $2 x$ .

$y = 2 x - 1$

Step 2

Use the slope-intercept form to find the slope and y-intercept.

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Step 2.1

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = 2$

$b = - 1$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $2$

y-intercept: $(0, - 1)$

Slope: $2$

y-intercept: $(0, - 1)$

Step 3