We first rewrite the line y - 3x = – 8 in slope-intercept form as:
y=3x-8.
The form y=mx+n is called the "slope-intercept form" because m tells us the slope and n tells us the y-intercept of the line.
Thus, the slope of the line is 3. We know that if a is the slope of any line perpendicular to our line, then the product of these slopes, 3a, is -1.
This means that the slope a is equal to -1/3. We are also given that the perpendicular line contains (3, 2). Thus, we write the equation:
[tex]y-2= -\frac{1}{3}(x-3)\\\\y-2=-\frac{1}{3}x+1\\\\y=-\frac{1}{3}x+3[/tex]
Answer: [tex]y=-\frac{1}{3}x+3[/tex]
