Please assist me in solving this problem

Question

Find K so that the line through (3,5) and (k,6) is perpendicular to 2y+5x=1

So i converted the given equation to y=5/2x+1/2

then i have found the slope of the perpendicular line to be -2/5.

Im now lost

Answer 1

Hello MS S,

You had a pretty good start, but you have made a minor sign error when you converted the equation to slope intercept form,

2y + 5x = 1

2y = -5x + 1

y = (-5/2)x + 1/2

You had a positive 5/2 which is an common error!

If the slope was 5/2, then you would be correct in saying that the slope of the perpendicular line is -2/5.

But, since the slope of the line is really -5/2, the slope of the perpendicular line is 2/5.

Now we need to find the value of k so that the slope of the line is 2/5

If the points are (3, 5) and (k, 6), then when we use the slope formula we would get (6 - 5)/(k - 3) This is the rise over the run, or the change in the y-coordinates divided by the change in the x-coordinates.

So, 1/(k - 3) = 2/5 . Then we solve for k.

2(k - 3) = 1(5) [It is hard to see, but I cross-multipled and set the products equat]

2k - 6 = 5

2k = 11

k = 11/2 or 5.5.

Hope this helps!

Jim

Answer 2

2y +5x =1

2y =-5x +1

y = -5x/2 + 1/2

slope =-5/2

slope of a perpendicular line is the negative inverse = +2/5

2/5 = (6-5)/(k-3) = 1/(k-3)

2/5 = 1/(k-3)

cross multiply

2k-6 =5

2k =11

k = 11/2 = 5.5

it may help to draw a sketch of the lines and points

the given line is y=-5x/2 + 1/2, with x intercept 1/5, y intercept 1/2, connect (1/5, 0) and (0, 1/2)

the perependicular lne is y =2x/5 + 3.8 with y intercept 3 4/5 connect (3,5) with (0, 3 4/5) and extend it in both directions, to intersect the 1st line and extend to the right to reach (5.5, 6)

set the equations equal and solve for fhe intersection point

or just sketch the lines and notice that (k,6) will have a higher x coordinate than (3,5)

5/2 x (6-5) + 3 = 5 1/2