Find k so that the line through ​(−5​,2​) and ​(k,4​) is​ a) parallel to 3y−2x=8​ ;​b) perpendicular to 2y+5x=7.

Answer 1

a) Can you see that the slope of the line 3y - 2x = 8 is 2/3?

The slope any parallel line will also 2/3.

(4 - 2)/(k -(-5)) = 2/3

(4 - 2)/(k + 5) = 2/3

2/(k + 5) = 2/3

k = -2

b) Can you see that the slope of the line 2y + 5x = 7 is -5/2?

The slope of any perpendicular line will be 2/5 which is the negative reciprocal.

(4 - 2)/(k -(-5)) = 2/5

(4 - 2)/(k + 5) = 2/5

2/(k + 5) = 2/5

k = 0