Question

Does someone mind helping me with this? Thank you!

Answer 1

`\displaystyle\\Answer:\ y=-(3)/(2)x+1`

Explanation:

The condition of perpendicularity of the two lines given by the equations:

`\displaystyle\\\left \{ {{y_1=m_1x+b_1} \atop {y_2=m_1x+b_2}} \right.`

is the relation: m₁ x m₂=-1

`\displaystyle\\Hence,\ m_2=-(1)/(m_1)`

`\displaystyle\\Given: y=(2)/(3)x+(2)/(3)\ == > \ m_1=(2)/(3) \\\\Thus,\ m_2=-(1)/((2)/(3) ) \\\\m_2=-(3)/(2)`

The equation of the Point-Slope Form is expressed as:

y-y₁=m(x-x₁)

(-2,4) that is x₁=-2 y₁=4

`\displaystyle\\Therefore,\\\ y-4=-(3)/(2) (x-(-2))\\\\y-4+4=-(3)/(2) (x+2)+4\\\\y=-(3)/(2)(x)-(3)/(2)(2) +4\\\\y=-(3)/(2)x -3+4\\\\y=-(3)/(2)x+1`

Answer 2

Try the slop formula. x1 - x2 over y1 - y2. Also, try to cross multiply what you already have.