Graph x-4y=-18

$x - 4 y = - 18$

Step 1

Solve for $y$ .

Subtract $x$ from both sides of the equation.

$- 4 y = - 18 - x$

Divide each term in $- 4 y = - 18 - x$ by $- 4$ and simplify.

Divide each term in $- 4 y = - 18 - x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{- 18}{- 4} + \frac{- x}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{- 18}{- 4} + \frac{- x}{- 4}$

Divide $y$ by $1$ .

$y = \frac{- 18}{- 4} + \frac{- x}{- 4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $- 18$ and $- 4$ .

Factor $- 2$ out of $- 18$ .

$y = \frac{- 2 (9)}{- 4} + \frac{- x}{- 4}$

Cancel the common factors.

Factor $- 2$ out of $- 4$ .

$y = \frac{- 2 \cdot 9}{- 2 \cdot 2} + \frac{- x}{- 4}$

Cancel the common factor.

$y = \frac{- 2 \cdot 9}{- 2 \cdot 2} + \frac{- x}{- 4}$

Rewrite the expression.

$y = \frac{9}{2} + \frac{- x}{- 4}$

Dividing two negative values results in a positive value.

$y = \frac{9}{2} + \frac{x}{4}$

Step 2

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Reorder $\frac{9}{2}$ and $\frac{x}{4}$ .

$y = \frac{x}{4} + \frac{9}{2}$

Reorder terms.

$y = \frac{1}{4} x + \frac{9}{2}$

Step 3

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

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

$m = \frac{1}{4}$

$b = \frac{9}{2}$

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

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{9}{2})$

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{9}{2})$

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.

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

Reorder $\frac{9}{2}$ and $\frac{x}{4}$ .

$y = \frac{x}{4} + \frac{9}{2}$

Reorder terms.

$y = \frac{1}{4} x + \frac{9}{2}$

Find the x-intercept.

To find the x-intercept(s), substitute in $0$ for $y$ and solve for $x$ .

$0 = \frac{1}{4} x + \frac{9}{2}$

Solve the equation.

Rewrite the equation as $\frac{1}{4} x + \frac{9}{2} = 0$ .

$\frac{1}{4} x + \frac{9}{2} = 0$

Combine $\frac{1}{4}$ and $x$ .

$\frac{x}{4} + \frac{9}{2} = 0$

Subtract $\frac{9}{2}$ from both sides of the equation.

$\frac{x}{4} = - \frac{9}{2}$

Multiply both sides of the equation by $4$ .

$4 \frac{x}{4} = 4 (- \frac{9}{2})$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$4 \frac{x}{4} = 4 (- \frac{9}{2})$

Rewrite the expression.

$x = 4 (- \frac{9}{2})$

Simplify the right side.

Simplify $4 (- \frac{9}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{9}{2}$ into the numerator.

$x = 4 (\frac{- 9}{2})$

Factor $2$ out of $4$ .

$x = 2 (2) \frac{- 9}{2}$

Cancel the common factor.

$x = 2 \cdot 2 \frac{- 9}{2}$

Rewrite the expression.

$x = 2 \cdot - 9$

Multiply $2$ by $- 9$ .

$x = - 18$

x-intercept(s) in point form.

x-intercept(s): $(- 18, 0)$

Find the y-intercept.

To find the y-intercept(s), substitute in $0$ for $x$ and solve for $y$ .

$y = \frac{1}{4} \cdot (0) + \frac{9}{2}$

Solve the equation.

Multiply $\frac{1}{4}$ by $0$ .

$y = \frac{1}{4} \cdot 0 + \frac{9}{2}$

Remove parentheses.

$y = \frac{1}{4} \cdot (0) + \frac{9}{2}$

Simplify $\frac{1}{4} \cdot (0) + \frac{9}{2}$ .

Multiply $\frac{1}{4}$ by $0$ .

$y = 0 + \frac{9}{2}$

Add $0$ and $\frac{9}{2}$ .

$y = \frac{9}{2}$

y-intercept(s) in point form.

y-intercept(s): $(0, \frac{9}{2})$

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

$\begin{array}{c} x & y \\ - 18 & 0 \\ 0 & \frac{9}{2} \end{array}$

Step 5

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

Slope: $\frac{1}{4}$

y-intercept: $(0, \frac{9}{2})$

$\begin{array}{c} x & y \\ - 18 & 0 \\ 0 & \frac{9}{2} \end{array}$

Step 6

Graph x-4y=-18

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