Find the Slope and y-intercept f(x)=4(1-3/5x)+8x

$f (x) = 4 (1 - \frac{3}{5} x) + 8 x$

Step 1

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 $4 (1 - \frac{3}{5} x) + 8 x$ .

Simplify each term.

Combine $x$ and $\frac{3}{5}$ .

$y = 4 (1 - \frac{x \cdot 3}{5}) + 8 x$

Move $3$ to the left of $x$ .

$y = 4 (1 - \frac{3 x}{5}) + 8 x$

Apply the distributive property.

$y = 4 \cdot 1 + 4 (- \frac{3 x}{5}) + 8 x$

Multiply $4$ by $1$ .

$y = 4 + 4 (- \frac{3 x}{5}) + 8 x$

Multiply $4 (- \frac{3 x}{5})$ .

Multiply $- 1$ by $4$ .

$y = 4 - 4 \frac{3 x}{5} + 8 x$

Combine $- 4$ and $\frac{3 x}{5}$ .

$y = 4 + \frac{- 4 (3 x)}{5} + 8 x$

Multiply $3$ by $- 4$ .

$y = 4 + \frac{- 12 x}{5} + 8 x$

Move the negative in front of the fraction.

$y = 4 - \frac{12 x}{5} + 8 x$

To write $8 x$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$y = 4 - \frac{12 x}{5} + 8 x \cdot \frac{5}{5}$

Simplify terms.

Combine $8 x$ and $\frac{5}{5}$ .

$y = 4 - \frac{12 x}{5} + \frac{8 x \cdot 5}{5}$

Combine the numerators over the common denominator.

$y = 4 + \frac{- 12 x + 8 x \cdot 5}{5}$

Simplify the numerator.

Factor $4 x$ out of $- 12 x + 8 x \cdot 5$ .

Factor $4 x$ out of $- 12 x$ .

$y = 4 + \frac{4 x (- 3) + 8 x \cdot 5}{5}$

Factor $4 x$ out of $8 x \cdot 5$ .

$y = 4 + \frac{4 x (- 3) + 4 x (2 \cdot 5)}{5}$

Factor $4 x$ out of $4 x (- 3) + 4 x (2 \cdot 5)$ .

$y = 4 + \frac{4 x (- 3 + 2 \cdot 5)}{5}$

Multiply $2$ by $5$ .

$y = 4 + \frac{4 x (- 3 + 10)}{5}$

Add $- 3$ and $10$ .

$y = 4 + \frac{4 x \cdot 7}{5}$

Multiply $7$ by $4$ .

$y = 4 + \frac{28 x}{5}$

Reorder $4$ and $\frac{28 x}{5}$ .

$y = \frac{28 x}{5} + 4$

Reorder terms.

$y = \frac{28}{5} x + 4$

Step 2

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

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

$m = \frac{28}{5}$

$b = 4$

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

Slope: $\frac{28}{5}$

y-intercept: $(0, 4)$

Slope: $\frac{28}{5}$

y-intercept: $(0, 4)$

Step 3

Find the Slope and y-intercept f(x)=4(1-3/5x)+8x

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