Question

Which of the following lines are perpendicular to the line y=-3x+ 5? (you may choose more than one answer)a. 3x-y=2b. y= 3x c. 3x+y=5d. 1/3x-y=3e. 3x-y=6

Answer 1

`d\text{. }(1)/(3)x-y=3`

Step-by-step explanation

2 lines are perpendicular if the product ot their slopes equals 1

then,

Step 1

find the slope of the given line

`\begin{gathered} y=-3x+5\Rightarrow y=mx+b \\ m\text{ is the slope} \end{gathered}`

so

`Slope_1_{}=-3`

Step 2

Now, let slope2 represents the slope of the line we are looking for ( perpendicular)

`\begin{gathered} \text{slope}_1\cdot slope_2=-1 \\ \text{replacing} \\ -3\cdot Slope_2=-1_{} \\ \text{divide both sides by -3} \\ (-3\cdot Slope_2)/(-3)=(-1)/(-3) \\ \text{Slope}_2=(1)/(3) \end{gathered}`

now, check in the answer options the function that has 1/3 as the factor of x

`\begin{gathered} y=mx+b \\ m=(1)/(3) \end{gathered}`

then, the answer is

`d\text{. }(1)/(3)x-y=3`