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