Question

write the slope-intercept equation of the function f whose graph satisfies the given conditions. the graph of f is perpendicular to the line whose equation is 4x - 3y - 9 = 0 and has the same y - intercept as this line. the equation of the function is \square. (use integers or fractions for any numbers in the equation.)

Explanation:

Step1: Find slope of given line

Rewrite $4x - 3y - 9 = 0$ to slope-intercept form $y=mx+b$:
$-3y = -4x + 9$
$y = \frac{4}{3}x - 3$
Slope of given line: $m_1 = \frac{4}{3}$

Step2: Find perpendicular slope

Perpendicular slope $m_2 = -\frac{1}{m_1}$
$m_2 = -\frac{3}{4}$

Step3: Identify shared y-intercept

From $y = \frac{4}{3}x - 3$, y-intercept $b = -3$

Step4: Write final equation

Use $y = m_2x + b$
$y = -\frac{3}{4}x - 3$

Answer:

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