Pre-Algebra Examples

$4 y + 6 = 0$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $6$ from both sides of the equation.

$4 y = - 6$

Step 1.2

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

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Step 1.2.1

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

$\frac{4 y}{4} = \frac{- 6}{4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 6}{4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6}{4}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

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

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Step 1.2.3.1.1

Factor $2$ out of $- 6$ .

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

Step 1.2.3.1.2

Cancel the common factors.

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Step 1.2.3.1.2.1

Factor $2$ out of $4$ .

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

Step 1.2.3.1.2.2

Cancel the common factor.

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

Step 1.2.3.1.2.3

Rewrite the expression.

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

Step 1.2.3.2

Move the negative in front of the fraction.

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

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 $y = m x + b$ .

$m = 0$

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

Step 2.3

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

Slope: $0$

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

Slope: $0$

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

Step 3

Find two points on the line.

$\begin{array}{c} x & y \\ 0 & - \frac{3}{2} \\ 1 & - \frac{3}{2} \end{array}$

Step 4

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

Slope: $0$

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

$\begin{array}{c} x & y \\ 0 & - \frac{3}{2} \\ 1 & - \frac{3}{2} \end{array}$

Step 5