Find the Slope and y-intercept q(x)=3(1-5/4x)+4x

$q (x) = 3 (1 - \frac{5}{4} x) + 4 x$

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 $3 (1 - \frac{5}{4} x) + 4 x$ .

Simplify each term.

Combine $x$ and $\frac{5}{4}$ .

$y = 3 (1 - \frac{x \cdot 5}{4}) + 4 x$

Move $5$ to the left of $x$ .

$y = 3 (1 - \frac{5 x}{4}) + 4 x$

Apply the distributive property.

$y = 3 \cdot 1 + 3 (- \frac{5 x}{4}) + 4 x$

Multiply $3$ by $1$ .

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

Multiply $3 (- \frac{5 x}{4})$ .

Multiply $- 1$ by $3$ .

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

Combine $- 3$ and $\frac{5 x}{4}$ .

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

Multiply $5$ by $- 3$ .

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

Move the negative in front of the fraction.

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

To write $4 x$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

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

Simplify terms.

Combine $4 x$ and $\frac{4}{4}$ .

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

Combine the numerators over the common denominator.

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

Simplify each term.

Simplify the numerator.

Factor $x$ out of $- 15 x + 4 x \cdot 4$ .

Factor $x$ out of $- 15 x$ .

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

Factor $x$ out of $4 x \cdot 4$ .

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

Factor $x$ out of $x \cdot - 15 + x (4 \cdot 4)$ .

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

Multiply $4$ by $4$ .

$y = 3 + \frac{x (- 15 + 16)}{4}$

Add $- 15$ and $16$ .

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

Multiply $x$ by $1$ .

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

Reorder $3$ and $\frac{x}{4}$ .

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

Reorder terms.

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

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

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

$m = \frac{1}{4}$

$b = 3$

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

Slope: $\frac{1}{4}$

y-intercept: $(0, 3)$

Slope: $\frac{1}{4}$

y-intercept: $(0, 3)$

Find the Slope and y-intercept q(x)=3(1-5/4x)+4x

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