Pre-Algebra Examples

$2 x = 10 - 2 y$

Step 1

Solve for $y$ .

Tap for more steps...

Step 1.1

Rewrite the equation as $10 - 2 y = 2 x$ .

$10 - 2 y = 2 x$

Step 1.2

Subtract $10$ from both sides of the equation.

$- 2 y = 2 x - 10$

Step 1.3

Divide each term in $- 2 y = 2 x - 10$ by $- 2$ and simplify.

Tap for more steps...

Step 1.3.1

Divide each term in $- 2 y = 2 x - 10$ by $- 2$ .

$\frac{- 2 y}{- 2} = \frac{2 x}{- 2} + \frac{- 10}{- 2}$

Step 1.3.2

Simplify the left side.

Tap for more steps...

Step 1.3.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{2 x}{- 2} + \frac{- 10}{- 2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{2 x}{- 2} + \frac{- 10}{- 2}$

Step 1.3.3

Simplify the right side.

Tap for more steps...

Step 1.3.3.1

Simplify each term.

Tap for more steps...

Step 1.3.3.1.1

Cancel the common factor of $2$ and $- 2$ .

Tap for more steps...

Step 1.3.3.1.1.1

Factor $2$ out of $2 x$ .

$y = \frac{2 (x)}{- 2} + \frac{- 10}{- 2}$

Step 1.3.3.1.1.2

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

$y = - 1 \cdot x + \frac{- 10}{- 2}$

Step 1.3.3.1.2

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

$y = - x + \frac{- 10}{- 2}$

Step 1.3.3.1.3

Divide $- 10$ by $- 2$ .

$y = - x + 5$

Step 2

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

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

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

$m = - 1$

$b = 5$

Step 2.3

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 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.

Tap for more steps...

Step 3.1

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

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

Step 4

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 5