Question

What is the equation of the line that is perpendicular to the given line and has an x-intercept of 6?

Answer 1

You did not include the "given line". You need the line to determine the slope of your line.

To calculate the slope of a line that is perpedicular to certain line, you must use the property that the product of the slope of two perpendicular lines is - 1.

So, the procedure is this:

1) Determine the slope of the given line (may be from the graph or from the equation,depending on the input information). Call this slope m1.

2) The slope, call it m2,  of the line that is perpendicular is calculated as:

m2 = - 1 /m1.

3) Now, you use such slope and the coordinates of the point given to find the equation of the perpedicular line.

In this case your point is the x-intercept, this is (6,0)

And you use this relation to find the equation:

y - 0
------- = m2
x - 6

From the choices given I can see that m2 is either - 1 or 1, so I am going to solve for both cases.

4) If m2 = 1 (which means that m1 = - 1),

y - 0
------ = 1
x - 6

=>  y - 0 = x - 6
=> y = x - 6 => the answer is the fourth option.

5) If m2 = - 1 (which means that m1 = 1),

y - 0
------- = - 1
x - 6

=> y - 0 = - (x - 6)
=> y = - x + 6 => the answer is the second option.

Neither y = - x + 8 nor y = x - 8 may be the right answer because their x-intercept is not 6 but 8.