Pre-Algebra Examples

$x = \frac{2 y}{21} + \frac{17}{21}$

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

Rewrite the equation as $\frac{2 y}{21} + \frac{17}{21} = x$ .

$\frac{2 y}{21} + \frac{17}{21} = x$

Step 1.3

Subtract $\frac{17}{21}$ from both sides of the equation.

$\frac{2 y}{21} = x - \frac{17}{21}$

Step 1.4

Multiply both sides of the equation by $\frac{21}{2}$ .

$\frac{21}{2} \cdot \frac{2 y}{21} = \frac{21}{2} (x - \frac{17}{21})$

Step 1.5

Simplify both sides of the equation.

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Step 1.5.1

Simplify the left side.

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Step 1.5.1.1

Simplify $\frac{21}{2} \cdot \frac{2 y}{21}$ .

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Step 1.5.1.1.1

Cancel the common factor of $21$ .

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Step 1.5.1.1.1.1

Cancel the common factor.

$\frac{21}{2} \cdot \frac{2 y}{21} = \frac{21}{2} (x - \frac{17}{21})$

Step 1.5.1.1.1.2

Rewrite the expression.

$\frac{1}{2} (2 y) = \frac{21}{2} (x - \frac{17}{21})$

Step 1.5.1.1.2

Cancel the common factor of $2$ .

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Step 1.5.1.1.2.1

Factor $2$ out of $2 y$ .

$\frac{1}{2} (2 (y)) = \frac{21}{2} (x - \frac{17}{21})$

Step 1.5.1.1.2.2

Cancel the common factor.

$\frac{1}{2} (2 y) = \frac{21}{2} (x - \frac{17}{21})$

Step 1.5.1.1.2.3

Rewrite the expression.

$y = \frac{21}{2} (x - \frac{17}{21})$

Step 1.5.2

Simplify the right side.

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Step 1.5.2.1

Simplify $\frac{21}{2} (x - \frac{17}{21})$ .

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Step 1.5.2.1.1

Apply the distributive property.

$y = \frac{21}{2} x + \frac{21}{2} (- \frac{17}{21})$

Step 1.5.2.1.2

Combine $\frac{21}{2}$ and $x$ .

$y = \frac{21 x}{2} + \frac{21}{2} (- \frac{17}{21})$

Step 1.5.2.1.3

Cancel the common factor of $21$ .

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Step 1.5.2.1.3.1

Move the leading negative in $- \frac{17}{21}$ into the numerator.

$y = \frac{21 x}{2} + \frac{21}{2} \cdot \frac{- 17}{21}$

Step 1.5.2.1.3.2

Cancel the common factor.

$y = \frac{21 x}{2} + \frac{21}{2} \cdot \frac{- 17}{21}$

Step 1.5.2.1.3.3

Rewrite the expression.

$y = \frac{21 x}{2} + \frac{1}{2} \cdot - 17$

Step 1.5.2.1.4

Combine $\frac{1}{2}$ and $- 17$ .

$y = \frac{21 x}{2} + \frac{- 17}{2}$

Step 1.5.2.1.5

Move the negative in front of the fraction.

$y = \frac{21 x}{2} - \frac{17}{2}$

Step 1.6

Reorder terms.

$y = \frac{21}{2} x - \frac{17}{2}$

Step 2

Using the slope-intercept form, the y-intercept is $- \frac{17}{2}$ .

$b = - \frac{17}{2}$

Step 3

y-intercept in point form.

$(0, - \frac{17}{2})$

Step 4