Find the Slope and y-intercept f(x)=5x-(4+7x)/3

$f (x) = 5 x - \frac{(4 + 7 x)}{3}$

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 $5 x - \frac{4 + 7 x}{3}$ .

To write $5 x$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$y = 5 x \cdot \frac{3}{3} - \frac{4 + 7 x}{3}$

Simplify terms.

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

$y = \frac{5 x \cdot 3}{3} - \frac{4 + 7 x}{3}$

Combine the numerators over the common denominator.

$y = \frac{5 x \cdot 3 - (4 + 7 x)}{3}$

Simplify the numerator.

Multiply $3$ by $5$ .

$y = \frac{15 x - (4 + 7 x)}{3}$

Apply the distributive property.

$y = \frac{15 x - 1 \cdot 4 - (7 x)}{3}$

Multiply $- 1$ by $4$ .

$y = \frac{15 x - 4 - (7 x)}{3}$

Multiply $7$ by $- 1$ .

$y = \frac{15 x - 4 - 7 x}{3}$

Subtract $7 x$ from $15 x$ .

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

Factor $4$ out of $8 x - 4$ .

Factor $4$ out of $8 x$ .

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

Factor $4$ out of $- 4$ .

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

Factor $4$ out of $4 (2 x) + 4 (- 1)$ .

$y = \frac{4 (2 x - 1)}{3}$

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

Apply the distributive property.

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

Multiply $2$ by $4$ .

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

Multiply $4$ by $- 1$ .

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

Split the fraction $\frac{8 x - 4}{3}$ into two fractions.

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

Move the negative in front of the fraction.

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

Reorder terms.

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

Step 2

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

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

$m = \frac{8}{3}$

$b = - \frac{4}{3}$

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

Slope: $\frac{8}{3}$

y-intercept: $(0, - \frac{4}{3})$

Slope: $\frac{8}{3}$

y-intercept: $(0, - \frac{4}{3})$

Step 3

Find the Slope and y-intercept f(x)=5x-(4+7x)/3

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