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

Answer:

$k=-\frac{1}{42}$

Step-by-step 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 $-\frac{1}{14}$ since that is its negative reciprocal.

In the equation $y=k*3x+2$, the slope would be 3k. 3k would be equal to $-\frac{1}{14}$:

$3k=-\frac{1}{14}$

Divide both sides by 3 to solve for k

$k=-\frac{1}{42}$

I hope this helps!