Algebra Examples

$0 = x + \frac{1}{4} y + \frac{1}{2}$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as $x + \frac{y}{4} + \frac{1}{2} = 0$ .

$x + \frac{y}{4} + \frac{1}{2} = 0$

Step 1.2

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

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Step 1.2.1

Subtract $x$ from both sides of the equation.

$\frac{y}{4} + \frac{1}{2} = - x$

Step 1.2.2

Subtract $\frac{1}{2}$ from both sides of the equation.

$\frac{y}{4} = - x - \frac{1}{2}$

Step 1.3

Multiply both sides of the equation by $4$ .

$4 \frac{y}{4} = 4 (- x - \frac{1}{2})$

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $4$ .

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Step 1.4.1.1.1

Cancel the common factor.

$4 \frac{y}{4} = 4 (- x - \frac{1}{2})$

Step 1.4.1.1.2

Rewrite the expression.

$y = 4 (- x - \frac{1}{2})$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $4 (- x - \frac{1}{2})$ .

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Step 1.4.2.1.1

Apply the distributive property.

$y = 4 (- x) + 4 (- \frac{1}{2})$

Step 1.4.2.1.2

Multiply $- 1$ by $4$ .

$y = - 4 x + 4 (- \frac{1}{2})$

Step 1.4.2.1.3

Cancel the common factor of $2$ .

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Step 1.4.2.1.3.1

Move the leading negative in $- \frac{1}{2}$ into the numerator.

$y = - 4 x + 4 (\frac{- 1}{2})$

Step 1.4.2.1.3.2

Factor $2$ out of $4$ .

$y = - 4 x + 2 (2) \frac{- 1}{2}$

Step 1.4.2.1.3.3

Cancel the common factor.

$y = - 4 x + 2 \cdot 2 \frac{- 1}{2}$

Step 1.4.2.1.3.4

Rewrite the expression.

$y = - 4 x + 2 \cdot - 1$

Step 1.4.2.1.4

Multiply $2$ by $- 1$ .

$y = - 4 x - 2$

Step 2

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

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Step 2.1

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 2.2

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

$m = - 4$

$b = - 2$

Step 2.3

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

Slope: $- 4$

y-intercept: $(0, - 2)$

Slope: $- 4$

y-intercept: $(0, - 2)$

Step 3

Any line can be graphed using two points. Select two $x$ values, and plug them into the equation to find the corresponding $y$ values.

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Step 3.1

Create a table of the $x$ and $y$ values.

$\begin{array}{c} x & y \\ 0 & - 2 \\ 1 & - 6 \end{array}$

Step 4

Graph the line using the slope and the y-intercept, or the points.

Slope: $- 4$

y-intercept: $(0, - 2)$

$\begin{array}{c} x & y \\ 0 & - 2 \\ 1 & - 6 \end{array}$

Step 5