Question

13 fill in the blank 1 point write the equation of a line that is perpendicular to y = 3x - 12 and passes through (6, -5). 1. m = (enter a number only.) 2. b = (enter a number only.) 3. equation = (enter your answer in the form y=mx+b)

Explanation:

Step1: Recall slope of perpendicular line

The slope of the given line \( y = 3x - 12 \) is \( m_1 = 3 \). For a line perpendicular to it, the slope \( m \) satisfies \( m\times m_1=- 1 \). So \( m=\frac{-1}{3} \) (as given).

Step2: Use point - slope form to find \( b \)

The point - slope form of a line is \( y - y_1=m(x - x_1) \), where \( (x_1,y_1)=(6,-5) \) and \( m =-\frac{1}{3} \).
Substitute the values: \( y-(-5)=-\frac{1}{3}(x - 6) \)
Simplify: \( y + 5=-\frac{1}{3}x+2 \)
Subtract 5 from both sides: \( y=-\frac{1}{3}x+2 - 5 \), so \( y=-\frac{1}{3}x-3 \). Here, \( m =-\frac{1}{3} \) and \( b=-3 \).

Step3: Write the equation

Using the slope - intercept form \( y = mx + b \) with \( m=-\frac{1}{3} \) and \( b = - 3 \), the equation is \( y=-\frac{1}{3}x-3 \).

Answer:

\( y=-\frac{1}{3}x - 3 \)