Question

The line x + 2y = 16 is perpendicular to a line containing the points (-9,n) and (1,5n). Find the value of n.

So how do I do it?

Answer 1

Step #1: Find the slope of the given line.

To do this, solve the equation for slope-intercept form:

x + 2y = 16

2y = -x + 16

y = -1/2 x +8

The slope of this line is -1/2.

Step #2: Find the slope of the new line.

To be perpendicular, the other line needs a slope that is the opposite reciprocal slope. So, that'd be +2/1 or just 2.

Step #3: Find n.

Now, you know m=2 and we also have the slope formula

m = (y2 - y1) / (x2 - x1)

Using the two points (-9,n) and (1,5n), we can set up:

2 = (5n - n) / (1 - (-9))

2 = 4n / 10

2 = 2n/5

Multiply by 5 and divide by 2:

10 = 2n

5 = n

The process was: find the slope of the given line, use that to find the slope of the perpendicular line, and then use and the slope formula to find n.