Pre-Algebra Examples

$3 (y + 1) - x = 6$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Subtract $3$ from both sides of the equation.

$3 y - x = 6 - 3$

Step 1.1.2

Add $x$ to both sides of the equation.

$3 y = 6 - 3 + x$

Step 1.1.3

Subtract $3$ from $6$ .

$3 y = 3 + x$

Step 1.2

Divide each term in $3 y = 3 + x$ by $3$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $3 y = 3 + x$ by $3$ .

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

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Cancel the common factor of $3$ .

Tap for more steps...

Step 1.2.2.1.1

Cancel the common factor.

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

Step 1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Divide $3$ by $3$ .

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

Step 2

Rewrite in slope-intercept form.

Tap for more steps...

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

Reorder $1$ and $\frac{x}{3}$ .

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

Step 2.3

Reorder terms.

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

Step 3

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

Tap for more steps...

Step 3.1

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

$m = \frac{1}{3}$

$b = 1$

Step 3.2

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

Slope: $\frac{1}{3}$

y-intercept: $(0, 1)$

Slope: $\frac{1}{3}$

y-intercept: $(0, 1)$

Step 4

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

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Reorder $1$ and $\frac{x}{3}$ .

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

Step 4.1.2

Reorder terms.

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

Step 4.2

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

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

Step 5

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

Slope: $\frac{1}{3}$

y-intercept: $(0, 1)$

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

Step 6