Algebra Examples

$g (x) = 3 (1 - \frac{5}{6} x) + 5 x$

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

Simplify the right side.

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Step 1.2.1

Simplify $3 (1 - \frac{5}{6} x) + 5 x$ .

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Step 1.2.1.1

Simplify each term.

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Step 1.2.1.1.1

Simplify each term.

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Step 1.2.1.1.1.1

Combine $x$ and $\frac{5}{6}$ .

$y = 3 (1 - \frac{x \cdot 5}{6}) + 5 x$

Step 1.2.1.1.1.2

Move $5$ to the left of $x$ .

$y = 3 (1 - \frac{5 x}{6}) + 5 x$

Step 1.2.1.1.2

Apply the distributive property.

$y = 3 \cdot 1 + 3 (- \frac{5 x}{6}) + 5 x$

Step 1.2.1.1.3

Multiply $3$ by $1$ .

$y = 3 + 3 (- \frac{5 x}{6}) + 5 x$

Step 1.2.1.1.4

Cancel the common factor of $3$ .

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Step 1.2.1.1.4.1

Move the leading negative in $- \frac{5 x}{6}$ into the numerator.

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

Step 1.2.1.1.4.2

Factor $3$ out of $6$ .

$y = 3 + 3 \frac{- 5 x}{3 (2)} + 5 x$

Step 1.2.1.1.4.3

Cancel the common factor.

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

Step 1.2.1.1.4.4

Rewrite the expression.

$y = 3 + \frac{- 5 x}{2} + 5 x$

Step 1.2.1.1.5

Move the negative in front of the fraction.

$y = 3 - \frac{5 x}{2} + 5 x$

Step 1.2.1.2

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

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

Step 1.2.1.3

Simplify terms.

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Step 1.2.1.3.1

Combine $5 x$ and $\frac{2}{2}$ .

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

Step 1.2.1.3.2

Combine the numerators over the common denominator.

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

Step 1.2.1.4

Simplify the numerator.

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Step 1.2.1.4.1

Factor $5 x$ out of $- 5 x + 5 x \cdot 2$ .

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Step 1.2.1.4.1.1

Factor $5 x$ out of $- 5 x$ .

$y = 3 + \frac{5 x (- 1) + 5 x \cdot 2}{2}$

Step 1.2.1.4.1.2

Factor $5 x$ out of $5 x \cdot 2$ .

$y = 3 + \frac{5 x (- 1) + 5 x (2)}{2}$

Step 1.2.1.4.1.3

Factor $5 x$ out of $5 x (- 1) + 5 x (2)$ .

$y = 3 + \frac{5 x (- 1 + 2)}{2}$

Step 1.2.1.4.2

Add $- 1$ and $2$ .

$y = 3 + \frac{5 x \cdot 1}{2}$

Step 1.2.1.4.3

Multiply $5$ by $1$ .

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

Step 1.3

Reorder $3$ and $\frac{5 x}{2}$ .

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

Step 1.4

Reorder terms.

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

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 $y = m x + b$ .

$m = \frac{5}{2}$

$b = 3$

Step 2.2

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

Slope: $\frac{5}{2}$

y-intercept: $(0, 3)$

Slope: $\frac{5}{2}$

y-intercept: $(0, 3)$

Step 3