Pre-Algebra Examples

$5 x = 6 y - 14$

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 $6 y - 14 = 5 x$ .

$6 y - 14 = 5 x$

Step 1.3

Add $14$ to both sides of the equation.

$6 y = 5 x + 14$

Step 1.4

Divide each term in $6 y = 5 x + 14$ by $6$ and simplify.

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Step 1.4.1

Divide each term in $6 y = 5 x + 14$ by $6$ .

$\frac{6 y}{6} = \frac{5 x}{6} + \frac{14}{6}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $6$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{5 x}{6} + \frac{14}{6}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{5 x}{6} + \frac{14}{6}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Cancel the common factor of $14$ and $6$ .

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Step 1.4.3.1.1

Factor $2$ out of $14$ .

$y = \frac{5 x}{6} + \frac{2 (7)}{6}$

Step 1.4.3.1.2

Cancel the common factors.

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Step 1.4.3.1.2.1

Factor $2$ out of $6$ .

$y = \frac{5 x}{6} + \frac{2 \cdot 7}{2 \cdot 3}$

Step 1.4.3.1.2.2

Cancel the common factor.

$y = \frac{5 x}{6} + \frac{2 \cdot 7}{2 \cdot 3}$

Step 1.4.3.1.2.3

Rewrite the expression.

$y = \frac{5 x}{6} + \frac{7}{3}$

Step 1.5

Reorder terms.

$y = \frac{5}{6} x + \frac{7}{3}$

Step 2

Using the slope-intercept form, the y-intercept is $\frac{7}{3}$ .

$b = \frac{7}{3}$

Step 3

y-intercept in point form.

$(0, \frac{7}{3})$

Step 4