What is the equation of the line that is perpendicular to the line y = -1/3x - 2 and passes through the point (3, 2)?

Answer 1

To find the equation of a perpendicular line, you first need to find the negative reciprocal of the slope given. The slope is -1/3, so the slope of the perpendicular line will be 3

Now we just need to find the y intercept using the point (3, 2) and you can plug the coordinates in and then solve for b. Let's see what that looks like.

y=3x+b

2=3*(3)+b

2=9+b

-7=b So now we know the y-intercept and slope. We just put them together now

y=3x-7

Hope this helps!

Brandon

Answer 2

Perpendicular lines have opposite reciprocal slopes. This means that the line perpendicular to y = -1/3x -2, which has a slope of -1/3x, will have a slope of 3 (the opposite reciprocal).

To ensure that the perpendicular line passes through (3,2) it is likely that the y-intercept (b) will need to change. So far we know that the perpendicular line will have the equation:

y = 3x + b

Now we can substitute the point (3,2) for y and x in the equation in order to solve for b.

y = 3x + b

2 = 3(3) + b

2 = 9 + b

-7 = b

Having found the slope and the y-intercept, the final equation of the perpendicular line is:

y = 3x -7

Answer 3

First off, what is the slope of the given line? Since that line is in slope-intercept form, we can see that its slope is -1/3. Now, the slope of a line perpendicular will be the opposite reciprocal, or 3. Now we need to make use of the other condition given, that the new line pass through (3, 2).

The easiest way to do this is to use point-slope form. y — y1 = m(x - x1). Plugging in: y — 2 = 3(x — 3). If we need to give our answer in slope-intercept form, distribute on the right and then add 2 to both sides.