Algebra Examples

$x - y = 4$ $x - 3 y = 0$

Step 1

Graph $x - y = 4$ .

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Step 1.1

Solve for $y$ .

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Step 1.1.1

Subtract $x$ from both sides of the equation.

$- y = 4 - x$

Step 1.1.2

Divide each term in $- y = 4 - x$ by $- 1$ and simplify.

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Step 1.1.2.1

Divide each term in $- y = 4 - x$ by $- 1$ .

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

Step 1.1.2.2

Simplify the left side.

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Step 1.1.2.2.1

Dividing two negative values results in a positive value.

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

Step 1.1.2.2.2

Divide $y$ by $1$ .

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

Step 1.1.2.3

Simplify the right side.

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Step 1.1.2.3.1

Simplify each term.

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Step 1.1.2.3.1.1

Divide $4$ by $- 1$ .

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

Step 1.1.2.3.1.2

Dividing two negative values results in a positive value.

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

Step 1.1.2.3.1.3

Divide $x$ by $1$ .

$y = - 4 + x$

Step 1.2

Rewrite in slope-intercept form.

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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 $- 4$ and $x$ .

$y = x - 4$

Step 1.3

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

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Step 1.3.1

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

$m = 1$

$b = - 4$

Step 1.3.2

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

Slope: $1$

y-intercept: $(0, - 4)$

Slope: $1$

y-intercept: $(0, - 4)$

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.

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Step 1.4.1

Reorder $- 4$ and $x$ .

$y = x - 4$

Step 1.4.2

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

$\begin{array}{c} x & y \\ 0 & - 4 \\ 1 & - 3 \end{array}$

Step 1.5

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

Slope: $1$

y-intercept: $(0, - 4)$

$\begin{array}{c} x & y \\ 0 & - 4 \\ 1 & - 3 \end{array}$

Slope: $1$

y-intercept: $(0, - 4)$

$\begin{array}{c} x & y \\ 0 & - 4 \\ 1 & - 3 \end{array}$

Step 2

Graph $x - 3 y = 0$ .

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Step 2.1

Solve for $y$ .

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Step 2.1.1

Subtract $x$ from both sides of the equation.

$- 3 y = - x$

Step 2.1.2

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

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Step 2.1.2.1

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

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

Step 2.1.2.2

Simplify the left side.

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Step 2.1.2.2.1

Cancel the common factor of $- 3$ .

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Step 2.1.2.2.1.1

Cancel the common factor.

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

Step 2.1.2.2.1.2

Divide $y$ by $1$ .

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

Step 2.1.2.3

Simplify the right side.

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Step 2.1.2.3.1

Dividing two negative values results in a positive value.

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

Step 2.2

Rewrite in slope-intercept form.

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Step 2.2.1

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 2.2.2

Reorder terms.

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

Step 2.3

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

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Step 2.3.1

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

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

$b = 0$

Step 2.3.2

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: $(0, 0)$

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

y-intercept: $(0, 0)$

Step 2.4

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

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Step 2.4.1

Reorder terms.

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

Step 2.4.2

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

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

Step 2.5

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

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

y-intercept: $(0, 0)$

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

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

y-intercept: $(0, 0)$

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

Step 3

Plot each graph on the same coordinate system.

$x - y = 4$

$x - 3 y = 0$

Step 4