Find the Slope and y-intercept f(x)=4(1-3/2x)+3x

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

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

Simplify each term.

Combine $x$ and $\frac{3}{2}$ .

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

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

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

Apply the distributive property.

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

Multiply $4$ by $1$ .

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

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{3 x}{2}$ into the numerator.

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

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

$y = 4 + 2 (- 3 x) + 3 x$

Multiply $- 3$ by $2$ .

$y = 4 - 6 x + 3 x$

Add $- 6 x$ and $3 x$ .

$y = 4 - 3 x$

Reorder $4$ and $- 3 x$ .

$y = - 3 x + 4$

Step 2

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

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

$m = - 3$

$b = 4$

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

Slope: $- 3$

y-intercept: $(0, 4)$

Slope: $- 3$

y-intercept: $(0, 4)$

Step 3