Question

what is the equation of the line that passes through the point (5, 4) and is perpendicular to the line y = 3x - 2? write your answer in slope - intercept form.
y = \square x + \square

Explanation:

Step1: Find slope of perpendicular line

The slope of \( y = 3x - 2 \) is \( 3 \). For perpendicular lines, slopes are negative reciprocals, so new slope \( m = -\frac{1}{3} \).

Step2: Use point - slope form

Point - slope formula: \( y - y_1 = m(x - x_1) \), with \( (x_1,y_1)=(5,4) \) and \( m = -\frac{1}{3} \).
Substitute: \( y - 4 = -\frac{1}{3}(x - 5) \).

Step3: Convert to slope - intercept

Expand: \( y - 4 = -\frac{1}{3}x+\frac{5}{3} \).
Add 4 (which is \( \frac{12}{3} \)): \( y = -\frac{1}{3}x+\frac{5 + 12}{3}=-\frac{1}{3}x+\frac{17}{3} \).

Answer:

\( y = -\frac{1}{3}x+\frac{17}{3} \) (So the first box is \( -\frac{1}{3} \) and the second box is \( \frac{17}{3} \))