Algebra Examples

Graph $16 x - 4 y = 2$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $16 x$ from both sides of the equation.

$- 4 y = 2 - 16 x$

Step 1.2

Divide each term in $- 4 y = 2 - 16 x$ by $- 4$ and simplify.

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Step 1.2.1

Divide each term in $- 4 y = 2 - 16 x$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{- 16 x}{- 4}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 4$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{2}{- 4} + \frac{- 16 x}{- 4}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{2}{- 4} + \frac{- 16 x}{- 4}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $2$ and $- 4$ .

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Step 1.2.3.1.1.1

Factor $2$ out of $2$ .

$y = \frac{2 (1)}{- 4} + \frac{- 16 x}{- 4}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $2$ out of $- 4$ .

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{- 16 x}{- 4}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 1}{2 \cdot - 2} + \frac{- 16 x}{- 4}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{1}{- 2} + \frac{- 16 x}{- 4}$

Step 1.2.3.1.2

Move the negative in front of the fraction.

$y = - \frac{1}{2} + \frac{- 16 x}{- 4}$

Step 1.2.3.1.3

Cancel the common factor of $- 16$ and $- 4$ .

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Step 1.2.3.1.3.1

Factor $- 4$ out of $- 16 x$ .

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

Step 1.2.3.1.3.2

Cancel the common factors.

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Step 1.2.3.1.3.2.1

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

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

Step 1.2.3.1.3.2.2

Cancel the common factor.

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

Step 1.2.3.1.3.2.3

Rewrite the expression.

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

Step 1.2.3.1.3.2.4

Divide $4 x$ by $1$ .

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

Step 2

Rewrite in slope-intercept form.

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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 $- \frac{1}{2}$ and $4 x$ .

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

Step 3

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

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Step 3.1

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

$m = 4$

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

Step 3.2

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

Slope: $4$

y-intercept: $(0, - \frac{1}{2})$

Slope: $4$

y-intercept: $(0, - \frac{1}{2})$

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.

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Step 4.1

Reorder $- \frac{1}{2}$ and $4 x$ .

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

Step 4.2

Find the x-intercept.

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Step 4.2.1

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

$0 = 4 x - \frac{1}{2}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

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

$4 x - \frac{1}{2} = 0$

Step 4.2.2.2

Add $\frac{1}{2}$ to both sides of the equation.

$4 x = \frac{1}{2}$

Step 4.2.2.3

Divide each term in $4 x = \frac{1}{2}$ by $4$ and simplify.

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Step 4.2.2.3.1

Divide each term in $4 x = \frac{1}{2}$ by $4$ .

$\frac{4 x}{4} = \frac{\frac{1}{2}}{4}$

Step 4.2.2.3.2

Simplify the left side.

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Step 4.2.2.3.2.1

Cancel the common factor of $4$ .

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Step 4.2.2.3.2.1.1

Cancel the common factor.

$\frac{4 x}{4} = \frac{\frac{1}{2}}{4}$

Step 4.2.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{\frac{1}{2}}{4}$

Step 4.2.2.3.3

Simplify the right side.

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Step 4.2.2.3.3.1

Multiply the numerator by the reciprocal of the denominator.

$x = \frac{1}{2} \cdot \frac{1}{4}$

Step 4.2.2.3.3.2

Multiply $\frac{1}{2} \cdot \frac{1}{4}$ .

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Step 4.2.2.3.3.2.1

Multiply $\frac{1}{2}$ by $\frac{1}{4}$ .

$x = \frac{1}{2 \cdot 4}$

Step 4.2.2.3.3.2.2

Multiply $2$ by $4$ .

$x = \frac{1}{8}$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s): $(\frac{1}{8}, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

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

$y = 4 (0) - \frac{1}{2}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Remove parentheses.

$y = 4 (0) - \frac{1}{2}$

Step 4.3.2.2

Simplify $4 (0) - \frac{1}{2}$ .

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Step 4.3.2.2.1

Multiply $4$ by $0$ .

$y = 0 - \frac{1}{2}$

Step 4.3.2.2.2

Subtract $\frac{1}{2}$ from $0$ .

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

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s): $(0, - \frac{1}{2})$

Step 4.4

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

$\begin{array}{c} x & y \\ 0 & - \frac{1}{2} \\ \frac{1}{8} & 0 \end{array}$

Step 5

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

Slope: $4$

y-intercept: $(0, - \frac{1}{2})$

$\begin{array}{c} x & y \\ 0 & - \frac{1}{2} \\ \frac{1}{8} & 0 \end{array}$

Step 6