Find the Slope and y-intercept r(x)=3(1-7/5x)+8x

$r (x) = 3 (1 - \frac{7}{5} x) + 8 x$

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 $3 (1 - \frac{7}{5} x) + 8 x$ .

Simplify each term.

Combine $x$ and $\frac{7}{5}$ .

$y = 3 (1 - \frac{x \cdot 7}{5}) + 8 x$

Move $7$ to the left of $x$ .

$y = 3 (1 - \frac{7 x}{5}) + 8 x$

Apply the distributive property.

$y = 3 \cdot 1 + 3 (- \frac{7 x}{5}) + 8 x$

Multiply $3$ by $1$ .

$y = 3 + 3 (- \frac{7 x}{5}) + 8 x$

Multiply $3 (- \frac{7 x}{5})$ .

Multiply $- 1$ by $3$ .

$y = 3 - 3 \frac{7 x}{5} + 8 x$

Combine $- 3$ and $\frac{7 x}{5}$ .

$y = 3 + \frac{- 3 (7 x)}{5} + 8 x$

Multiply $7$ by $- 3$ .

$y = 3 + \frac{- 21 x}{5} + 8 x$

Move the negative in front of the fraction.

$y = 3 - \frac{21 x}{5} + 8 x$

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

$y = 3 - \frac{21 x}{5} + 8 x \cdot \frac{5}{5}$

Simplify terms.

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

$y = 3 - \frac{21 x}{5} + \frac{8 x \cdot 5}{5}$

Combine the numerators over the common denominator.

$y = 3 + \frac{- 21 x + 8 x \cdot 5}{5}$

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 21 x + 8 x \cdot 5$ .

Factor $x$ out of $- 21 x$ .

$y = 3 + \frac{x \cdot - 21 + 8 x \cdot 5}{5}$

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

$y = 3 + \frac{x \cdot - 21 + x (8 \cdot 5)}{5}$

Factor $x$ out of $x \cdot - 21 + x (8 \cdot 5)$ .

$y = 3 + \frac{x (- 21 + 8 \cdot 5)}{5}$

Multiply $8$ by $5$ .

$y = 3 + \frac{x (- 21 + 40)}{5}$

Add $- 21$ and $40$ .

$y = 3 + \frac{x \cdot 19}{5}$

Move $19$ to the left of $x$ .

$y = 3 + \frac{19 x}{5}$

Reorder $3$ and $\frac{19 x}{5}$ .

$y = \frac{19 x}{5} + 3$

Reorder terms.

$y = \frac{19}{5} x + 3$

Step 2

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

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

$m = \frac{19}{5}$

$b = 3$

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

Slope: $\frac{19}{5}$

y-intercept: $(0, 3)$

Slope: $\frac{19}{5}$

y-intercept: $(0, 3)$

Step 3

Find the Slope and y-intercept r(x)=3(1-7/5x)+8x

Related Questions

Support LCMGCF.com by disabling your adblocker.