Pre-Algebra Examples

$5 x = 7 y + 19$

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 $7 y + 19 = 5 x$ .

$7 y + 19 = 5 x$

Step 1.3

Subtract $19$ from both sides of the equation.

$7 y = 5 x - 19$

Step 1.4

Divide each term in $7 y = 5 x - 19$ by $7$ and simplify.

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Step 1.4.1

Divide each term in $7 y = 5 x - 19$ by $7$ .

$\frac{7 y}{7} = \frac{5 x}{7} + \frac{- 19}{7}$

Step 1.4.2

Simplify the left side.

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Step 1.4.2.1

Cancel the common factor of $7$ .

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Step 1.4.2.1.1

Cancel the common factor.

$\frac{7 y}{7} = \frac{5 x}{7} + \frac{- 19}{7}$

Step 1.4.2.1.2

Divide $y$ by $1$ .

$y = \frac{5 x}{7} + \frac{- 19}{7}$

Step 1.4.3

Simplify the right side.

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Step 1.4.3.1

Move the negative in front of the fraction.

$y = \frac{5 x}{7} - \frac{19}{7}$

Step 1.5

Reorder terms.

$y = \frac{5}{7} x - \frac{19}{7}$

Step 2

Using the slope-intercept form, the slope is $\frac{5}{7}$ .

$m = \frac{5}{7}$

Step 3