Question

Please help :) I have no clue & math isn’t my strong subject.

Answer 1

Equation of a line that is perpendicular to given line is
`y=(-7)/(4) x+(7)/(4)`.

Equation of a line that is parallel to given line is
`y=(4)/(7) x-(69)/(7)`.

Solution:

Given line
`y=(4)/(7) x+4`.

Slope of this line,
`m_1` =
`(4)/(7)`

`$\text{Slope of perpendicular line} = \frac{-1}{\text{Slope of the given line} }`

`$m_2=(-1)/(m_1)`

`$=(-1)/((4)/(7) )`

Slope of perpendicular line,
`m_2=(-7)/(4)`

Passes through the point (–7, 5). Here
`x_1=-7, y_1=5`.

Point-slope formula:

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

`$y-(-7)=(-7)/(4) (x-5)`

`$y+7=(-7)/(4) x+(35)/(4)`

Subtract 7 from both sides, we get

`$y=(-7)/(4) x+(7)/(4)`

Equation of a line that is perpendicular to given line is
`y=(-7)/(4) x+(7)/(4)`.

To find the parallel line:

Slopes of parallel lines are equal.

`m_1=m_3`

`$m_3=(4)/(7)`

Passes through the point (–7, 5). Here
`x_1=-7, y_1=5`.

Point-slope formula:

`$y-(-7)=(4)/(7) (x-5)`

`$y+7=(4)/(7) x-(20)/(7)`

Subtract 7 from both sides,

`$y=(4)/(7) x-(69)/(7)`

Equation of a line that is parallel to given line is
`y=(4)/(7) x-(69)/(7)`.