Algebra Examples

3 x - 5 y = 10

$3 x - 5 y = 10$

Step 1

Solve for

y

$y$ .

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Step 1.1

Subtract

3 x

$3 x$ from both sides of the equation.

- 5 y = 10 - 3 x

$- 5 y = 10 - 3 x$

Step 1.2

Divide each term in

- 5 y = 10 - 3 x

$- 5 y = 10 - 3 x$ by

- 5

$- 5$ and simplify.

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Step 1.2.1

Divide each term in

- 5 y = 10 - 3 x

$- 5 y = 10 - 3 x$ by

- 5

$- 5$ .

\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 3 x}{- 5}

$\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 3 x}{- 5}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of

- 5

$- 5$ .

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Step 1.2.2.1.1

Cancel the common factor.

\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 3 x}{- 5}

$\frac{- 5 y}{- 5} = \frac{10}{- 5} + \frac{- 3 x}{- 5}$

Step 1.2.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{10}{- 5} + \frac{- 3 x}{- 5}

$y = \frac{10}{- 5} + \frac{- 3 x}{- 5}$

y = \frac{10}{- 5} + \frac{- 3 x}{- 5}

$y = \frac{10}{- 5} + \frac{- 3 x}{- 5}$

y = \frac{10}{- 5} + \frac{- 3 x}{- 5}

$y = \frac{10}{- 5} + \frac{- 3 x}{- 5}$

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

Divide

10

$10$ by

- 5

$- 5$ .

y = - 2 + \frac{- 3 x}{- 5}

$y = - 2 + \frac{- 3 x}{- 5}$

Step 1.2.3.1.2

Dividing two negative values results in a positive value.

y = - 2 + \frac{3 x}{5}

$y = - 2 + \frac{3 x}{5}$

y = - 2 + \frac{3 x}{5}

$y = - 2 + \frac{3 x}{5}$

y = - 2 + \frac{3 x}{5}

$y = - 2 + \frac{3 x}{5}$

y = - 2 + \frac{3 x}{5}

$y = - 2 + \frac{3 x}{5}$

y = - 2 + \frac{3 x}{5}

$y = - 2 + \frac{3 x}{5}$

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

- 2

$- 2$ and

\frac{3 x}{5}

$\frac{3 x}{5}$ .

y = \frac{3 x}{5} - 2

$y = \frac{3 x}{5} - 2$

Step 2.3

Reorder terms.

y = \frac{3}{5} x - 2

$y = \frac{3}{5} x - 2$

y = \frac{3}{5} x - 2

$y = \frac{3}{5} x - 2$

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

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = \frac{3}{5}

$m = \frac{3}{5}$

b = - 2

$b = - 2$

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{3}{5}

$\frac{3}{5}$

y-intercept:

(0, - 2)

$(0, - 2)$

Slope:

\frac{3}{5}

$\frac{3}{5}$

y-intercept:

(0, - 2)

$(0, - 2)$

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

- 2

$- 2$ and

\frac{3 x}{5}

$\frac{3 x}{5}$ .

y = \frac{3 x}{5} - 2

$y = \frac{3 x}{5} - 2$

Step 4.1.2

Reorder terms.

y = \frac{3}{5} x - 2

$y = \frac{3}{5} x - 2$

y = \frac{3}{5} x - 2

$y = \frac{3}{5} x - 2$

Step 4.2

Create a table of the

x

$x$ and

y

$y$ values.

\begin{array}{c} x & y \\ 0 & - 2 \\ 5 & 1 \end{array}

$\begin{array}{c} x & y \\ 0 & - 2 \\ 5 & 1 \end{array}$

\begin{array}{c} x & y \\ 0 & - 2 \\ 5 & 1 \end{array}

$\begin{array}{c} x & y \\ 0 & - 2 \\ 5 & 1 \end{array}$

Step 5

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

Slope:

\frac{3}{5}

$\frac{3}{5}$

y-intercept:

(0, - 2)

$(0, - 2)$

\begin{array}{c} x & y \\ 0 & - 2 \\ 5 & 1 \end{array}

$\begin{array}{c} x & y \\ 0 & - 2 \\ 5 & 1 \end{array}$

Step 6