Pre-Algebra Examples

$0.3 - 7 y = 5.1 x$

Step 1

Rewrite in slope-intercept form.

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Step 1.1

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 1.2

Subtract

$0.3$ from both sides of the equation.

$- 7 y = 5.1 x - 0.3$

Step 1.3

Divide each term in

$- 7 y = 5.1 x - 0.3$ by

$- 7$ and simplify.

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Step 1.3.1

Divide each term in

$- 7 y = 5.1 x - 0.3$ by

$- 7$ .

$\frac{- 7 y}{- 7} = \frac{5.1 x}{- 7} + \frac{- 0.3}{- 7}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of

$- 7$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{- 7 y}{- 7} = \frac{5.1 x}{- 7} + \frac{- 0.3}{- 7}$

Step 1.3.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{5.1 x}{- 7} + \frac{- 0.3}{- 7}$

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

Move the negative in front of the fraction.

$y = - \frac{5.1 x}{7} + \frac{- 0.3}{- 7}$

Step 1.3.3.1.2

Factor

$5.1$ out of

$5.1 x$ .

$y = - \frac{5.1 (x)}{7} + \frac{- 0.3}{- 7}$

Step 1.3.3.1.3

Factor

$7$ out of

$7$ .

$y = - \frac{5.1 (x)}{7 (1)} + \frac{- 0.3}{- 7}$

Step 1.3.3.1.4

Separate fractions.

$y = - (\frac{5.1}{7} \cdot \frac{x}{1}) + \frac{- 0.3}{- 7}$

Step 1.3.3.1.5

Divide

$5.1$ by

$7$ .

$y = - (0.7\overline{285714} \frac{x}{1}) + \frac{- 0.3}{- 7}$

Step 1.3.3.1.6

Divide

$x$ by

$1$ .

$y = - (0.7\overline{285714} x) + \frac{- 0.3}{- 7}$

Step 1.3.3.1.7

Multiply

$0.7\overline{285714}$ by

$- 1$ .

$y = - 0.7\overline{285714} x + \frac{- 0.3}{- 7}$

Step 1.3.3.1.8

Divide

$- 0.3$ by

$- 7$ .

$y = - 0.7\overline{285714} x + 0.0\overline{428571}$

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

$m$ and

$b$ using the form

$y = m x + b$ .

$m = - 0.7\overline{285714}$

$b = 0.0\overline{428571}$

Step 2.2

The slope of the line is the value of

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

$b$ .

Slope:

$- 0.7\overline{285714}$

y-intercept:

$(0, 0.0\overline{428571})$

Slope:

$- 0.7\overline{285714}$

y-intercept:

$(0, 0.0\overline{428571})$

Step 3