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

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

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

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

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

Simplify terms.

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

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

Combine the numerators over the common denominator.

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

Simplify the numerator.

Multiply $5$ by $5$ .

$y = \frac{25 x - (4 + 7 x)}{5}$

Apply the distributive property.

$y = \frac{25 x - 1 \cdot 4 - (7 x)}{5}$

Multiply $- 1$ by $4$ .

$y = \frac{25 x - 4 - (7 x)}{5}$

Multiply $7$ by $- 1$ .

$y = \frac{25 x - 4 - 7 x}{5}$

Subtract $7 x$ from $25 x$ .

$y = \frac{18 x - 4}{5}$

Factor $2$ out of $18 x - 4$ .

Factor $2$ out of $18 x$ .

$y = \frac{2 (9 x) - 4}{5}$

Factor $2$ out of $- 4$ .

$y = \frac{2 (9 x) + 2 (- 2)}{5}$

Factor $2$ out of $2 (9 x) + 2 (- 2)$ .

$y = \frac{2 (9 x - 2)}{5}$

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

Apply the distributive property.

$y = \frac{2 (9 x) + 2 \cdot - 2}{5}$

Multiply $9$ by $2$ .

$y = \frac{18 x + 2 \cdot - 2}{5}$

Multiply $2$ by $- 2$ .

$y = \frac{18 x - 4}{5}$

Split the fraction $\frac{18 x - 4}{5}$ into two fractions.

$y = \frac{18 x}{5} + \frac{- 4}{5}$

Move the negative in front of the fraction.

$y = \frac{18 x}{5} - \frac{4}{5}$

Reorder terms.

$y = \frac{18}{5} x - \frac{4}{5}$

Step 2

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

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

$m = \frac{18}{5}$

$b = - \frac{4}{5}$

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

Slope: $\frac{18}{5}$

y-intercept: $(0, - \frac{4}{5})$

Slope: $\frac{18}{5}$

y-intercept: $(0, - \frac{4}{5})$

Step 3

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

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