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

Answer:

k = 5.

Step-by-step 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.