Question

Find the value of k given that the line through (k, 2) and (7, 0) is perpendicular to the line y=x−285.

Answer 1

k = 5.

Explanation:

Equation of a line:

The equation of a line has the following format:

`y = mx + b`

In which m is the slope, and b is the y-intercept(y when x = 0).

Perpendicular lines

When two lines are perpendicular, the multiplication of their slopes is -1.

Perpendicular to the line y=x−285.

This line has slope 1, so the line we want to find the equation has slope
`m = -1`

Then

`y = -x + b`

Passes through (7, 0)

This means that when
`x = 7, y = 0`. So

`y = -x + b`

`0 = -7 + b`

`b = 7`

So

`y = -x + 7`

Find the value of k given that the line through (k, 2)

This means that when
`x = k, y = 2`. So

`y = -x + 7`

`2 = -k + 7`

`k = 7 - 2 = 5`

The value of k is k = 5.