Question

Determine the value of "k" when the lines y=k3x+2 and y=14x+2 are perpendicular. Show your work. (3 marks/PS)

Answer 1

`k=-(1)/(42)`

Explanation:

Hi there!

What we need to know:

• Slope-intercept form:
  `y=mx+b` where m is the slope and b is the y-intercept (the value of y when x is 0)
• Perpendicular lines always have slopes that are negative reciprocals (ex. 2 and -1/2)

Given the equation
`y=14x+2`, we can identify the slope (m) to be 14. This means that the slope of a perpendicular line would have to be
`-(1)/(14)` since that is its negative reciprocal.

In the equation
`y=k*3x+2`, the slope would be 3k. 3k would be equal to
`-(1)/(14)`:

`3k=-(1)/(14)`

Divide both sides by 3 to solve for k

`k=-(1)/(42)`

I hope this helps!