Find the Slope and y-intercept r(x)=(7x-15)-(-17+4x)

$r (x) = (7 x - 15) - (- 17 + 4 x)$

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 $(7 x - 15) - (- 17 + 4 x)$ .

Simplify each term.

Apply the distributive property.

$y = 7 x - 15 - - 17 - (4 x)$

Multiply $- 1$ by $- 17$ .

$y = 7 x - 15 + 17 - (4 x)$

Multiply $4$ by $- 1$ .

$y = 7 x - 15 + 17 - 4 x$

Simplify by adding terms.

Subtract $4 x$ from $7 x$ .

$y = 3 x - 15 + 17$

Add $- 15$ and $17$ .

$y = 3 x + 2$

Step 2

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

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

$m = 3$

$b = 2$

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

Slope: $3$

y-intercept: $(0, 2)$

Slope: $3$

y-intercept: $(0, 2)$

Step 3