Question

write the equation of a line perpendicular to the line that passes through the given point.
`y = - 5x - (4)/(3)`(6,-4)

Answer 1

The equation of a line perpendicular to the line that passes through the given point as;

`y=(x)/(5)-(26)/(5)`

Step-by-step explanation:

Given that we want to find the eqution of the line perpendicular to the line equation below;

`y=-5x-(4)/(3)`

Whose slope is;

`m_1=-5`

For two lines to be perpendicular, the slope must follow the rule below;

`\begin{gathered} m_1.m_2=-1 \\ m_2=(-1)/(m_1) \end{gathered}`

Substituting the value of the given slope;

`\begin{gathered} m_2=(-1)/(m_1)=(-1)/(-5) \\ m_2=(1)/(5) \end{gathered}`

Now we have the slope of our line.

We can now derive the equation using the point-slope equation of line;

`y-y_1=m(x-x_1)`

With the given point;

`(x_1,y_1)=(6,-4)`

Substituting the slope and the given point, we have;

`\begin{gathered} y-y_1=m(x-x_1) \\ y-(-4)=(1)/(5)(x-6) \\ y+4=(x)/(5)-(6)/(5) \\ y=(x)/(5)-(6)/(5)-4 \\ y=(x)/(5)-(26)/(5) \end{gathered}`

Therefore, we have the equation of a line perpendicular to the line that passes through the given point as;

`y=(x)/(5)-(26)/(5)`