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

k = 5.

Step-by-step explanation:

Equation of a line:

The equation of a line has the following format:

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

Then

Passes through (7, 0)

This means that when . So

So

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

This means that when . So

The value of k is k = 5.

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step-by-step explanation: