Question

Find the equation of a line perpendicular to y - 3x = – 8 that passes through the point (3, 2). (answer in slope-intercept form)

A) y = -3x + 2
B) y = -3x + 3
C) y = - 1/3 x + 2
D) y = - 1/3 x + 3

Answer 1

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:


`y-2= -(1)/(3)(x-3)\\\\y-2=-(1)/(3)x+1\\\\y=-(1)/(3)x+3`

Answer:
`y=-(1)/(3)x+3`