Algebra Examples

4 x - y = 7

$4 x - y = 7$

Step 1

Solve for

$y$ .

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Step 1.1

Subtract

$4 x$ from both sides of the equation.

$- y = 7 - 4 x$

Step 1.2

Divide each term in

$- y = 7 - 4 x$ by

$- 1$ and simplify.

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Step 1.2.1

Divide each term in

$- y = 7 - 4 x$ by

$- 1$ .

$\frac{- y}{- 1} = \frac{7}{- 1} + \frac{- 4 x}{- 1}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{7}{- 1} + \frac{- 4 x}{- 1}$

Step 1.2.2.2

Divide

$y$ by

$1$ .

$y = \frac{7}{- 1} + \frac{- 4 x}{- 1}$

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

$7$ by

$- 1$ .

$y = - 7 + \frac{- 4 x}{- 1}$

Step 1.2.3.1.2

Move the negative one from the denominator of

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

$y = - 7 - 1 \cdot (- 4 x)$

Step 1.2.3.1.3

Rewrite

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

$- (- 4 x)$ .

$y = - 7 - (- 4 x)$

Step 1.2.3.1.4

Multiply

$- 4$ by

$- 1$ .

$y = - 7 + 4 x$

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

$- 7$ and

$4 x$ .

$y = 4 x - 7$

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

$y = m x + b$ .

$m = 4$

$b = - 7$

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:

$(0, - 7)$

Slope:

$4$

y-intercept:

$(0, - 7)$

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

$- 7$ and

$4 x$ .

$y = 4 x - 7$

Step 4.2

Create a table of the

$x$ and

$y$ values.

$\begin{array}{c} x & y \\ 0 & - 7 \\ 1 & - 3 \end{array}$

Step 5

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

Slope:

$4$

y-intercept:

$(0, - 7)$

$\begin{array}{c} x & y \\ 0 & - 7 \\ 1 & - 3 \end{array}$

Step 6