Answer:
[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]
Step-by-step explanation:
1. Calculate the slope of Line f
y - 3 = -⁹/₄(x – 6)
The coefficient of x is -⁹/₄, so
The slope m₁ = -⁹/₄.
2. Calculate the slope of the perpendicular line
m₂ = -1/m₁
m₂ = ⁴/₉
3. Calculate the y-intercept of line g
y = mx + b
4 = 6(⁴/₉) + b
4 = ⁸/₃ + b
Subtract ⁸/₃ from each side: b = 4 - ⁸/₃ = ⁴/₃
The y-intercept is b = ⁴/₃.
Step 4. Write the equation for line g
[tex]\boxed{ y = \frac{ 4}{ 9}x + \frac{4 }{3 }}[/tex]
The Figure below shows the graph of line f in red, and the graph of its perpendicular line g in black.
