Find the Slope and y-intercept g(x)=2(2-10/3x)+6x

$g (x) = 2 (2 - \frac{10}{3} x) + 6 x$

Rewrite in slope-intercept form.

The slope-intercept form is $y = m x + b$ , where $m$ is the slope and $b$ is the y-intercept.

$y = m x + b$

Simplify the right side.

Simplify $2 (2 - \frac{10}{3} x) + 6 x$ .

Simplify each term.

Combine $x$ and $\frac{10}{3}$ .

$y = 2 (2 - \frac{x \cdot 10}{3}) + 6 x$

Move $10$ to the left of $x$ .

$y = 2 (2 - \frac{10 x}{3}) + 6 x$

Apply the distributive property.

$y = 2 \cdot 2 + 2 (- \frac{10 x}{3}) + 6 x$

Multiply $2$ by $2$ .

$y = 4 + 2 (- \frac{10 x}{3}) + 6 x$

Multiply $2 (- \frac{10 x}{3})$ .

Multiply $- 1$ by $2$ .

$y = 4 - 2 \frac{10 x}{3} + 6 x$

Combine $- 2$ and $\frac{10 x}{3}$ .

$y = 4 + \frac{- 2 (10 x)}{3} + 6 x$

Multiply $10$ by $- 2$ .

$y = 4 + \frac{- 20 x}{3} + 6 x$

Move the negative in front of the fraction.

$y = 4 - \frac{20 x}{3} + 6 x$

To write $6 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 4 - \frac{20 x}{3} + 6 x \cdot \frac{3}{3}$

Simplify terms.

Combine $6 x$ and $\frac{3}{3}$ .

$y = 4 - \frac{20 x}{3} + \frac{6 x \cdot 3}{3}$

Combine the numerators over the common denominator.

$y = 4 + \frac{- 20 x + 6 x \cdot 3}{3}$

Simplify each term.

Simplify the numerator.

Factor $2 x$ out of $- 20 x + 6 x \cdot 3$ .

Factor $2 x$ out of $- 20 x$ .

$y = 4 + \frac{2 x (- 10) + 6 x \cdot 3}{3}$

Factor $2 x$ out of $6 x \cdot 3$ .

$y = 4 + \frac{2 x (- 10) + 2 x (3 \cdot 3)}{3}$

Factor $2 x$ out of $2 x (- 10) + 2 x (3 \cdot 3)$ .

$y = 4 + \frac{2 x (- 10 + 3 \cdot 3)}{3}$

Multiply $3$ by $3$ .

$y = 4 + \frac{2 x (- 10 + 9)}{3}$

Add $- 10$ and $9$ .

$y = 4 + \frac{2 x \cdot - 1}{3}$

Multiply $- 1$ by $2$ .

$y = 4 + \frac{- 2 x}{3}$

Move the negative in front of the fraction.

$y = 4 - \frac{2 x}{3}$

Reorder $4$ and $- \frac{2 x}{3}$ .

$y = - \frac{2 x}{3} + 4$

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

Reorder terms.

$y = - (\frac{2}{3} x) + 4$

Remove parentheses.

$y = - \frac{2}{3} x + 4$

Use the slope-intercept form to find the slope and y-intercept.

Find the values of $m$ and $b$ using the form $y = m x + b$ .

$m = - \frac{2}{3}$

$b = 4$

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

Slope: $- \frac{2}{3}$

y-intercept: $(0, 4)$

Slope: $- \frac{2}{3}$

y-intercept: $(0, 4)$

Find the Slope and y-intercept g(x)=2(2-10/3x)+6x

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