Algebra Examples

2 x - 4 y = 8

$2 x - 4 y = 8$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 1.2

Subtract

2 x

$2 x$ from both sides of the equation.

- 4 y = 8 - 2 x

$- 4 y = 8 - 2 x$

Step 1.3

Divide each term in

- 4 y = 8 - 2 x

$- 4 y = 8 - 2 x$ by

- 4

$- 4$ and simplify.

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Step 1.3.1

Divide each term in

- 4 y = 8 - 2 x

$- 4 y = 8 - 2 x$ by

- 4

$- 4$ .

\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 2 x}{- 4}

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

- 4

$- 4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{8}{- 4} + \frac{- 2 x}{- 4}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide

$8$ by

$- 4$ .

$y = - 2 + \frac{- 2 x}{- 4}$

Step 1.3.3.1.2

Cancel the common factor of

$- 2$ and

$- 4$ .

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Step 1.3.3.1.2.1

Factor

$- 2$ out of

$- 2 x$ .

$y = - 2 + \frac{- 2 (x)}{- 4}$

Step 1.3.3.1.2.2

Cancel the common factors.

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Step 1.3.3.1.2.2.1

Factor

$- 2$ out of

$- 4$ .

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

Step 1.3.3.1.2.2.2

Cancel the common factor.

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

Step 1.3.3.1.2.2.3

Rewrite the expression.

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

Step 1.4

Write in

$y = m x + b$ form.

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Step 1.4.1

Reorder

$- 2$ and

$\frac{x}{2}$ .

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

Step 1.4.2

Reorder terms.

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

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

$y = m x + b$ .

$m = \frac{1}{2}$

$b = - 2$

Step 2.2

The slope of the line is the value of

$m$ , and the y-intercept is the value of

$b$ .

Slope:

$\frac{1}{2}$

y-intercept:

$(0, - 2)$

Slope:

$\frac{1}{2}$

y-intercept:

$(0, - 2)$

Step 3