Algebra Examples

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

Step 1

Graph $x + 2 y = 4$ .

Tap for more steps...

Step 1.1

Solve for $y$ .

Tap for more steps...

Step 1.1.1

Subtract $x$ from both sides of the equation.

$2 y = 4 - x$

Step 1.1.2

Divide each term in $2 y = 4 - x$ by $2$ and simplify.

Tap for more steps...

Step 1.1.2.1

Divide each term in $2 y = 4 - x$ by $2$ .

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

Step 1.1.2.2

Simplify the left side.

Tap for more steps...

Step 1.1.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 1.1.2.2.1.1

Cancel the common factor.

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

Step 1.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 1.1.2.3

Simplify the right side.

Tap for more steps...

Step 1.1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.1.2.3.1.1

Divide $4$ by $2$ .

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

Step 1.1.2.3.1.2

Move the negative in front of the fraction.

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

Step 1.2

Rewrite in slope-intercept form.

Tap for more steps...

Step 1.2.1

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 1.2.2

Reorder $2$ and $- \frac{x}{2}$ .

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

Step 1.2.3

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

Tap for more steps...

Step 1.2.3.1

Reorder terms.

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

Step 1.2.3.2

Remove parentheses.

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

Step 1.3

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

Tap for more steps...

Step 1.3.1

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

$m = - \frac{1}{2}$

$b = 2$

Step 1.3.2

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

Step 1.4

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 1.4.1

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

Tap for more steps...

Step 1.4.1.1

Reorder $2$ and $- \frac{x}{2}$ .

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

Step 1.4.1.2

Reorder terms.

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

Step 1.4.1.3

Remove parentheses.

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

Step 1.4.2

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

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

Step 1.5

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

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

Slope: $- \frac{1}{2}$

y-intercept: $(0, 2)$

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

Step 2

Plot each graph on the same coordinate system.

$x + 2 y = 4$

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

Step 3