Algebra Examples

x - 6 y = 7

$x - 6 y = 7$

Step 1

Solve for

y

$y$ .

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Step 1.1

Subtract

x

$x$ from both sides of the equation.

- 6 y = 7 - x

$- 6 y = 7 - x$

Step 1.2

Divide each term in

- 6 y = 7 - x

$- 6 y = 7 - x$ by

- 6

$- 6$ and simplify.

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Step 1.2.1

Divide each term in

- 6 y = 7 - x

$- 6 y = 7 - x$ by

- 6

$- 6$ .

\frac{- 6 y}{- 6} = \frac{7}{- 6} + \frac{- x}{- 6}

$\frac{- 6 y}{- 6} = \frac{7}{- 6} + \frac{- x}{- 6}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of

- 6

$- 6$ .

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Step 1.2.2.1.1

Cancel the common factor.

\frac{- 6 y}{- 6} = \frac{7}{- 6} + \frac{- x}{- 6}

$\frac{- 6 y}{- 6} = \frac{7}{- 6} + \frac{- x}{- 6}$

Step 1.2.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{7}{- 6} + \frac{- x}{- 6}

$y = \frac{7}{- 6} + \frac{- x}{- 6}$

y = \frac{7}{- 6} + \frac{- x}{- 6}

$y = \frac{7}{- 6} + \frac{- x}{- 6}$

y = \frac{7}{- 6} + \frac{- x}{- 6}

$y = \frac{7}{- 6} + \frac{- x}{- 6}$

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

Move the negative in front of the fraction.

y = - \frac{7}{6} + \frac{- x}{- 6}

$y = - \frac{7}{6} + \frac{- x}{- 6}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

y = - \frac{7}{6} + \frac{x}{6}

$y = - \frac{7}{6} + \frac{x}{6}$

y = - \frac{7}{6} + \frac{x}{6}

$y = - \frac{7}{6} + \frac{x}{6}$

y = - \frac{7}{6} + \frac{x}{6}

$y = - \frac{7}{6} + \frac{x}{6}$

y = - \frac{7}{6} + \frac{x}{6}

$y = - \frac{7}{6} + \frac{x}{6}$

y = - \frac{7}{6} + \frac{x}{6}

$y = - \frac{7}{6} + \frac{x}{6}$

Step 2

Rewrite in slope-intercept form.

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Step 2.1

The slope-intercept form is

y = m x + b

$y = m x + b$ , where

m

$m$ is the slope and

b

$b$ is the y-intercept.

y = m x + b

$y = m x + b$

Step 2.2

Reorder

- \frac{7}{6}

$- \frac{7}{6}$ and

\frac{x}{6}

$\frac{x}{6}$ .

y = \frac{x}{6} - \frac{7}{6}

$y = \frac{x}{6} - \frac{7}{6}$

Step 2.3

Reorder terms.

y = \frac{1}{6} x - \frac{7}{6}

$y = \frac{1}{6} x - \frac{7}{6}$

y = \frac{1}{6} x - \frac{7}{6}

$y = \frac{1}{6} x - \frac{7}{6}$

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

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = \frac{1}{6}

$m = \frac{1}{6}$

b = - \frac{7}{6}

$b = - \frac{7}{6}$

Step 3.2

The slope of the line is the value of

m

$m$ , and the y-intercept is the value of

b

$b$ .

Slope:

\frac{1}{6}

$\frac{1}{6}$

y-intercept:

(0, - \frac{7}{6})

$(0, - \frac{7}{6})$

Slope:

\frac{1}{6}

$\frac{1}{6}$

y-intercept:

(0, - \frac{7}{6})

$(0, - \frac{7}{6})$

Step 4

Any line can be graphed using two points. Select two

x

$x$ values, and plug them into the equation to find the corresponding

y

$y$ values.

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Step 4.1

Write in

y = m x + b

$y = m x + b$ form.

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Step 4.1.1

Reorder

- \frac{7}{6}

$- \frac{7}{6}$ and

\frac{x}{6}

$\frac{x}{6}$ .

y = \frac{x}{6} - \frac{7}{6}

$y = \frac{x}{6} - \frac{7}{6}$

Step 4.1.2

Reorder terms.

y = \frac{1}{6} x - \frac{7}{6}

$y = \frac{1}{6} x - \frac{7}{6}$

y = \frac{1}{6} x - \frac{7}{6}

$y = \frac{1}{6} x - \frac{7}{6}$

Step 4.2

Find the x-intercept.

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Step 4.2.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

0 = \frac{1}{6} x - \frac{7}{6}

$0 = \frac{1}{6} x - \frac{7}{6}$

Step 4.2.2

Solve the equation.

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Step 4.2.2.1

Rewrite the equation as

\frac{1}{6} x - \frac{7}{6} = 0

$\frac{1}{6} x - \frac{7}{6} = 0$ .

\frac{1}{6} x - \frac{7}{6} = 0

$\frac{1}{6} x - \frac{7}{6} = 0$

Step 4.2.2.2

Combine

\frac{1}{6}

$\frac{1}{6}$ and

x

$x$ .

\frac{x}{6} - \frac{7}{6} = 0

$\frac{x}{6} - \frac{7}{6} = 0$

Step 4.2.2.3

Add

\frac{7}{6}

$\frac{7}{6}$ to both sides of the equation.

\frac{x}{6} = \frac{7}{6}

$\frac{x}{6} = \frac{7}{6}$

Step 4.2.2.4

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

x = 7

$x = 7$

x = 7

$x = 7$

Step 4.2.3

x-intercept(s) in point form.

x-intercept(s):

(7, 0)

$(7, 0)$

x-intercept(s):

(7, 0)

$(7, 0)$

Step 4.3

Find the y-intercept.

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Step 4.3.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

y = \frac{1}{6} \cdot (0) - \frac{7}{6}

$y = \frac{1}{6} \cdot (0) - \frac{7}{6}$

Step 4.3.2

Solve the equation.

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Step 4.3.2.1

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

0

$0$ .

y = \frac{1}{6} \cdot 0 - \frac{7}{6}

$y = \frac{1}{6} \cdot 0 - \frac{7}{6}$

Step 4.3.2.2

Remove parentheses.

y = \frac{1}{6} \cdot (0) - \frac{7}{6}

$y = \frac{1}{6} \cdot (0) - \frac{7}{6}$

Step 4.3.2.3

Simplify

\frac{1}{6} \cdot (0) - \frac{7}{6}

$\frac{1}{6} \cdot (0) - \frac{7}{6}$ .

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Step 4.3.2.3.1

Multiply

\frac{1}{6}

$\frac{1}{6}$ by

0

$0$ .

y = 0 - \frac{7}{6}

$y = 0 - \frac{7}{6}$

Step 4.3.2.3.2

Subtract

\frac{7}{6}

$\frac{7}{6}$ from

0

$0$ .

y = - \frac{7}{6}

$y = - \frac{7}{6}$

y = - \frac{7}{6}

$y = - \frac{7}{6}$

y = - \frac{7}{6}

$y = - \frac{7}{6}$

Step 4.3.3

y-intercept(s) in point form.

y-intercept(s):

(0, - \frac{7}{6})

$(0, - \frac{7}{6})$

y-intercept(s):

(0, - \frac{7}{6})

$(0, - \frac{7}{6})$

Step 4.4

Create a table of the

x

$x$ and

y

$y$ values.

\begin{array}{c} x & y \\ 0 & - \frac{7}{6} \\ 7 & 0 \end{array}

$\begin{array}{c} x & y \\ 0 & - \frac{7}{6} \\ 7 & 0 \end{array}$

\begin{array}{c} x & y \\ 0 & - \frac{7}{6} \\ 7 & 0 \end{array}

$\begin{array}{c} x & y \\ 0 & - \frac{7}{6} \\ 7 & 0 \end{array}$

Step 5

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

Slope:

\frac{1}{6}

$\frac{1}{6}$

y-intercept:

(0, - \frac{7}{6})

$(0, - \frac{7}{6})$

\begin{array}{c} x & y \\ 0 & - \frac{7}{6} \\ 7 & 0 \end{array}

$\begin{array}{c} x & y \\ 0 & - \frac{7}{6} \\ 7 & 0 \end{array}$

Step 6

x - 6 y = 7

$x - 6 y = 7$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$