Pre-Algebra Examples

$7 x + 8 y = 18$

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 $7 x$ from both sides of the equation.

$8 y = 18 - 7 x$

Step 1.3

Divide each term in $8 y = 18 - 7 x$ by $8$ and simplify.

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Step 1.3.1

Divide each term in $8 y = 18 - 7 x$ by $8$ .

$\frac{8 y}{8} = \frac{18}{8} + \frac{- 7 x}{8}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $8$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{18}{8} + \frac{- 7 x}{8}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{18}{8} + \frac{- 7 x}{8}$

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

Cancel the common factor of $18$ and $8$ .

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Step 1.3.3.1.1.1

Factor $2$ out of $18$ .

$y = \frac{2 (9)}{8} + \frac{- 7 x}{8}$

Step 1.3.3.1.1.2

Cancel the common factors.

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Step 1.3.3.1.1.2.1

Factor $2$ out of $8$ .

$y = \frac{2 \cdot 9}{2 \cdot 4} + \frac{- 7 x}{8}$

Step 1.3.3.1.1.2.2

Cancel the common factor.

$y = \frac{2 \cdot 9}{2 \cdot 4} + \frac{- 7 x}{8}$

Step 1.3.3.1.1.2.3

Rewrite the expression.

$y = \frac{9}{4} + \frac{- 7 x}{8}$

Step 1.3.3.1.2

Move the negative in front of the fraction.

$y = \frac{9}{4} - \frac{7 x}{8}$

Step 1.4

Write in $y = m x + b$ form.

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Step 1.4.1

Reorder $\frac{9}{4}$ and $- \frac{7 x}{8}$ .

$y = - \frac{7 x}{8} + \frac{9}{4}$

Step 1.4.2

Reorder terms.

$y = - (\frac{7}{8} x) + \frac{9}{4}$

Step 1.4.3

Remove parentheses.

$y = - \frac{7}{8} x + \frac{9}{4}$

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 $y = m x + b$ .

$m = - \frac{7}{8}$

$b = \frac{9}{4}$

Step 2.2

The slope of the line is the value of $m$ , and the y-intercept is the value of $b$ .

Slope: $- \frac{7}{8}$

y-intercept: $(0, \frac{9}{4})$

Slope: $- \frac{7}{8}$

y-intercept: $(0, \frac{9}{4})$

Step 3