Question

Hi can you give me the basic answer for 12 please

Answer 1

Given the equation of the line:

`y=-5x-(1)/(2)`

• You can identify that it is written in Slope-Intercept Form:

`y=mx+b`

Where "m" is the slope of the line, and "b" is the y-intercept.

Notice that:

`\begin{gathered} m_1=-5 \\ b_1=-(1)/(2) \end{gathered}`

• By definition, parallel lines have the same slope, but their y-intercepts are different.

Therefore, you can determine that the slope of the line parallel to the first line is:

`m_2=-5`

You know that this line passes through this point:

`(-4,2)`

Therefore, substituting the slope and the coordinates of that point into this equation:

`y=m_2x+b_2`

And solving for the y-intercept, you get:

`\begin{gathered} 2=(-5)(-4)+b_2 \\ \\ 2-20=b_2 \\ \\ b_2=-18\frac{}{} \end{gathered}`

Then, the equation of the line parallel to the first line is:

`y=-5x-18`

• By definition, the slopes of perpendicular lines are opposite reciprocal, therefore, the slope of this line is:

`m_3=(1)/(5)`

Using the same procedure used before to find the y-intercept, you get:

`\begin{gathered} 2=((1)/(5))(-4)+b_3 \\ \\ 2+(2)/(5)=b_3 \\ \\ b_3=(14)/(5) \end{gathered}`

Therefore, its equation is:

`y=(1)/(5)x+(14)/(5)`

Hence, the answer is:

- Equation for the parallel line:

`y=-5x-18`

- Equation for the perpendicular line:

`y=(1)/(5)x+(14)/(5)`