If a line through the points (8, 2 and (-2, y) is perpendicular to the line 5x + 8y=34 find the value of y.

Question

 please.help. im clueless

Answer 1

The line (Standard Format) 5x+8y=34 has slope of (-A/B) = -5/8.  All perpendicular lines have slope of 8/5 and an equation that looks like:  8x-5y=C.

 

Solve for C using point (8,2):

      8(8)-5(2) = C

          54 = C

The equation for the line is:    8x - 5y = 54

 

The point (-2,y) is on the line; what is y?

     8(-2)-5y = 54

        -5y = 70

          y = -14

Answer 2

5x+8y=34

8y=-5x+34

y=(-5/8)x+(34/8)

the slope of this line is -5/8

the slope of the line perpendicular to this line is the negative reciprocal of -5/8

the negative reciprocal is 8/5

the perpendicular line has slope 8/5 and goes through the points (8,2) and (-2,y)

find the slope of the line using the two given points and set it equal to 8/5

(y-2)/(-2-8)=8/5

(y-2)/(-10)=8/5

there are different approaches from here

one approach is to cross multiply

5(y-2)=8(-10)

5y-10=-80

5y=-80+10

5y=-70

y=-70/5

y=-14 (answer)

another approach:

8/5=(y-2)/(-10)

8(-2)/5(-2)=(y-2)/(-10)

-16/-10=(y-2)/-10

-16=y-2

y=-16+2

y=-14 again