Question

what is the slope of line perpendicular to Y=3x-2 translated 3 units down? A: y=5x. B: 2 C: y=x-2. D: y=6x-2

Answer 1

Answer:$\begin{gathered} \text{The new slope is -1/3} \\ \text{The new equation is y = }\frac{-1}{3}x-5(\text{considering the 3 units downward translation)} \end{gathered}$

Explanations:

The general equation of a line is given by:

y = mx + c..............(1)

Where m = the slope and

c = the intercept

The first given equation is:

y = 3x - 2

Comparing the above with the general equation (i.e. equation 1)

m = 3 , c = -2

For a line to be perpendicular to another line, it must have a slope that is a negative inverse of the line:

Therefore the line that is perpendicular to line y = 3x - 2 will have a slope:

$m_2\text{ = }\frac{-1}{m}=\frac{-1}{3}$

The new line that is perpendicular to the first line will have the equation:

$\begin{gathered} y=m_2x\text{ + c} \\ y\text{ = }\frac{-1}{3}x\text{ + (-2)} \\ y\text{ = }\frac{-1}{3}x\text{ - 2} \end{gathered}$

Since the line is translated 3 units down, the equation becomes:

$\begin{gathered} y\text{ = }\frac{-1}{3}x\text{ -2 - 3} \\ y\text{ = }\frac{-1}{3}x\text{ - 5} \end{gathered}$