Algebra Examples

$2 x + 4 y = 6$

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

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

$4 y = 6 - 2 x$

Step 1.3

Divide each term in $4 y = 6 - 2 x$ by $4$ and simplify.

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Step 1.3.1

Divide each term in $4 y = 6 - 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{6}{4} + \frac{- 2 x}{4}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $4$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{6}{4} + \frac{- 2 x}{4}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{4} + \frac{- 2 x}{4}$

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

Cancel the common factor of $6$ and $4$ .

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Step 1.3.3.1.1.1

Factor $2$ out of $6$ .

$y = \frac{2 (3)}{4} + \frac{- 2 x}{4}$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $2$ out of $4$ .

$y = \frac{2 \cdot 3}{2 \cdot 2} + \frac{- 2 x}{4}$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 3}{2 \cdot 2} + \frac{- 2 x}{4}$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{3}{2} + \frac{- 2 x}{4}$

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 $- 2 x$ .

$y = \frac{3}{2} + \frac{2 (- x)}{4}$

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 $4$ .

$y = \frac{3}{2} + \frac{2 (- x)}{2 (2)}$

Step 1.3.3.1.2.2.2

Cancel the common factor.

$y = \frac{3}{2} + \frac{2 (- x)}{2 \cdot 2}$

Step 1.3.3.1.2.2.3

Rewrite the expression.

$y = \frac{3}{2} + \frac{- x}{2}$

Step 1.3.3.1.3

Move the negative in front of the fraction.

$y = \frac{3}{2} - \frac{x}{2}$

Step 1.4

Write in $y = m x + b$ form.

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Step 1.4.1

Reorder $\frac{3}{2}$ and $- \frac{x}{2}$ .

$y = - \frac{x}{2} + \frac{3}{2}$

Step 1.4.2

Reorder terms.

$y = - (\frac{1}{2} x) + \frac{3}{2}$

Step 1.4.3

Remove parentheses.

$y = - \frac{1}{2} x + \frac{3}{2}$

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 $y = m x + b$ .

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

$b = \frac{3}{2}$

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: $(0, \frac{3}{2})$

Slope: $- \frac{1}{2}$

y-intercept: $(0, \frac{3}{2})$

Step 3