Algebra Examples

4 x - y = 5

$4 x - y = 5$

Step 1

Solve for

y

$y$ .

Tap for more steps...

Step 1.1

Subtract

4 x

$4 x$ from both sides of the equation.

- y = 5 - 4 x

$- y = 5 - 4 x$

Step 1.2

Divide each term in

- y = 5 - 4 x

$- y = 5 - 4 x$ by

- 1

$- 1$ and simplify.

Tap for more steps...

Step 1.2.1

Divide each term in

- y = 5 - 4 x

$- y = 5 - 4 x$ by

- 1

$- 1$ .

\frac{- y}{- 1} = \frac{5}{- 1} + \frac{- 4 x}{- 1}

$\frac{- y}{- 1} = \frac{5}{- 1} + \frac{- 4 x}{- 1}$

Step 1.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.1

Dividing two negative values results in a positive value.

\frac{y}{1} = \frac{5}{- 1} + \frac{- 4 x}{- 1}

$\frac{y}{1} = \frac{5}{- 1} + \frac{- 4 x}{- 1}$

Step 1.2.2.2

Divide

y

$y$ by

1

$1$ .

y = \frac{5}{- 1} + \frac{- 4 x}{- 1}

$y = \frac{5}{- 1} + \frac{- 4 x}{- 1}$

y = \frac{5}{- 1} + \frac{- 4 x}{- 1}

$y = \frac{5}{- 1} + \frac{- 4 x}{- 1}$

Step 1.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.3.1

Simplify each term.

Tap for more steps...

Step 1.2.3.1.1

Divide

5

$5$ by

- 1

$- 1$ .

y = - 5 + \frac{- 4 x}{- 1}

$y = - 5 + \frac{- 4 x}{- 1}$

Step 1.2.3.1.2

Move the negative one from the denominator of

\frac{- 4 x}{- 1}

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

y = - 5 - 1 \cdot (- 4 x)

$y = - 5 - 1 \cdot (- 4 x)$

Step 1.2.3.1.3

Rewrite

- 1 \cdot (- 4 x)

$- 1 \cdot (- 4 x)$ as

- (- 4 x)

$- (- 4 x)$ .

y = - 5 - (- 4 x)

$y = - 5 - (- 4 x)$

Step 1.2.3.1.4

Multiply

- 4

$- 4$ by

- 1

$- 1$ .

y = - 5 + 4 x

$y = - 5 + 4 x$

y = - 5 + 4 x

$y = - 5 + 4 x$

y = - 5 + 4 x

$y = - 5 + 4 x$

y = - 5 + 4 x

$y = - 5 + 4 x$

y = - 5 + 4 x

$y = - 5 + 4 x$

Step 2

Rewrite in slope-intercept form.

Tap for more steps...

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

- 5

$- 5$ and

4 x

$4 x$ .

y = 4 x - 5

$y = 4 x - 5$

y = 4 x - 5

$y = 4 x - 5$

Step 3

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

Tap for more steps...

Step 3.1

Find the values of

m

$m$ and

b

$b$ using the form

y = m x + b

$y = m x + b$ .

m = 4

$m = 4$

b = - 5

$b = - 5$

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:

4

$4$

y-intercept:

(0, - 5)

$(0, - 5)$

Slope:

4

$4$

y-intercept:

(0, - 5)

$(0, - 5)$

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.

Tap for more steps...

Step 4.1

Reorder

- 5

$- 5$ and

4 x

$4 x$ .

y = 4 x - 5

$y = 4 x - 5$

Step 4.2

Create a table of the

x

$x$ and

y

$y$ values.

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

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

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

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

Step 5

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

Slope:

4

$4$

y-intercept:

(0, - 5)

$(0, - 5)$

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

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

Step 6