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

Question

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

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1 year 2021-09-04T10:58:02+00:00 1 Answers 1 views 0

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

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!