Pre-Algebra Examples

$- 3 x - 3 y = - 15$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Add $3 x$ to both sides of the equation.

$- 3 y = - 15 + 3 x$

Step 1.2

Divide each term in $- 3 y = - 15 + 3 x$ by $- 3$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in $- 3 y = - 15 + 3 x$ by $- 3$ .

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3} + \frac{3 x}{- 3}$

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.

$\frac{- 3 y}{- 3} = \frac{- 15}{- 3} + \frac{3 x}{- 3}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 15}{- 3} + \frac{3 x}{- 3}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Divide $- 15$ by $- 3$ .

$y = 5 + \frac{3 x}{- 3}$

Step 1.2.3.1.2

Cancel the common factor of $3$ and $- 3$ .

Tap for more steps...

Step 1.2.3.1.2.1

Factor $3$ out of $3 x$ .

$y = 5 + \frac{3 (x)}{- 3}$

Step 1.2.3.1.2.2

Move the negative one from the denominator of $\frac{x}{- 1}$ .

$y = 5 - 1 \cdot x$

Step 1.2.3.1.3

Rewrite $- 1 \cdot x$ as $- x$ .

$y = 5 - x$

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 $5$ and $- x$ .

$y = - x + 5$

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 $y = m x + b$ .

$m = - 1$

$b = 5$

Step 3.2

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

Slope: $- 1$

y-intercept: $(0, 5)$

Slope: $- 1$

y-intercept: $(0, 5)$

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

Reorder $5$ and $- x$ .

$y = - x + 5$

Step 4.2

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

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 4 \end{array}$

Step 5

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

Slope: $- 1$

y-intercept: $(0, 5)$

$\begin{array}{c} x & y \\ 0 & 5 \\ 1 & 4 \end{array}$

Step 6