Algebra Examples

3 x - y = 2

$3 x - y = 2$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Subtract

3 x

$3 x$ from both sides of the equation.

- y = 2 - 3 x

$- y = 2 - 3 x$

Step 1.3

Divide each term in

- y = 2 - 3 x

$- y = 2 - 3 x$ by

- 1

$- 1$ and simplify.

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Step 1.3.1

Divide each term in

- y = 2 - 3 x

$- y = 2 - 3 x$ by

- 1

$- 1$ .

\frac{- y}{- 1} = \frac{2}{- 1} + \frac{- 3 x}{- 1}

$\frac{- y}{- 1} = \frac{2}{- 1} + \frac{- 3 x}{- 1}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Dividing two negative values results in a positive value.

\frac{y}{1} = \frac{2}{- 1} + \frac{- 3 x}{- 1}

$\frac{y}{1} = \frac{2}{- 1} + \frac{- 3 x}{- 1}$

Step 1.3.2.2

Divide

y

$y$ by

1

$1$ .

y = \frac{2}{- 1} + \frac{- 3 x}{- 1}

$y = \frac{2}{- 1} + \frac{- 3 x}{- 1}$

y = \frac{2}{- 1} + \frac{- 3 x}{- 1}

$y = \frac{2}{- 1} + \frac{- 3 x}{- 1}$

Step 1.3.3

Simplify the right side.

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Step 1.3.3.1

Simplify each term.

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Step 1.3.3.1.1

Divide

2

$2$ by

- 1

$- 1$ .

y = - 2 + \frac{- 3 x}{- 1}

$y = - 2 + \frac{- 3 x}{- 1}$

Step 1.3.3.1.2

Move the negative one from the denominator of

\frac{- 3 x}{- 1}

$\frac{- 3 x}{- 1}$ .

y = - 2 - 1 \cdot (- 3 x)

$y = - 2 - 1 \cdot (- 3 x)$

Step 1.3.3.1.3

Rewrite

- 1 \cdot (- 3 x)

$- 1 \cdot (- 3 x)$ as

- (- 3 x)

$- (- 3 x)$ .

y = - 2 - (- 3 x)

$y = - 2 - (- 3 x)$

Step 1.3.3.1.4

Multiply

- 3

$- 3$ by

- 1

$- 1$ .

y = - 2 + 3 x

$y = - 2 + 3 x$

y = - 2 + 3 x

$y = - 2 + 3 x$

y = - 2 + 3 x

$y = - 2 + 3 x$

y = - 2 + 3 x

$y = - 2 + 3 x$

Step 1.4

Reorder

- 2

$- 2$ and

3 x

$3 x$ .

y = 3 x - 2

$y = 3 x - 2$

y = 3 x - 2

$y = 3 x - 2$

Step 2

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

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Step 2.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = 3

$m = 3$

b = - 2

$b = - 2$

Step 2.2

The slope of the line is the value of

m

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

b

$b$ .

Slope:

3

$3$

y-intercept:

(0, - 2)

$(0, - 2)$

Slope:

3

$3$

y-intercept:

(0, - 2)

$(0, - 2)$

Step 3