Question

Find the value of k given that the line through (k,2) and (7,0) is perpendicular to the line y=x-28/5

Answer 1

y = x - 28/5. The slope here is 1. A perpendicular line will have a negative reciprocal slope. So our perpendicular line will have a slope of -1.

slope = (y2 - y1) / (x2 - x1)
(k,2)....x1 = k and y1 = 2
(7,0)...x2 = 7 and y2 = 0
sub
slope = (0 - 2) / (7 - k)
slope = -2 / ?......now if we want the slope to be -1..that means the number where the question mark is has to be 2....for that to happen, k has to be 5...because 7 - 5 = 2.

so ur answer is : k = 5

Answer 2

(5,2) would be the K value for the line.

Explanation:

Remember that perpendicular lines have inverse slopes, this means that they have the same number but with different signs, the line y=x-28/5 has a slope of 1 since 1 is the number that is multiplying the x, so the slope of the perpendicular line should be -1.

To calculate the value of K we need to use the formula for slope:

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

We insert the values into the formula and clear for K:

`m=(y2-y1)/(x2-x1)\\m=(0-2)/(7-k)\\-1(7-k)=-2\\k=-2+7\\k=5`

So now we know that the value of K would be 5.