Question

Two points A(0,-4), B(2,-1)determine line AB.What is the equation of the line AB? y= _1_x + _2_What is the equation of the line perpendicular to lineAB, passing through the point (2,-1)? y= _3_x + _4

Answer 1

1.

Let:

`\begin{gathered} (x1,y1)=(0,-4) \\ (x2,y2)=(2,-1) \\ so\colon \\ m1=(y2-y1)/(x2-x1)=(-1-(-4))/(2-0)=(3)/(2) \end{gathered}`

Using the point-slope equation:

`\begin{gathered} y-y1=m1(x-x1) \\ y-(-4)=(3)/(2)(x-0) \\ y+4=(3)/(2)x \\ y=(3)/(2)x-4 \end{gathered}`

2.

If two lines are perpendicular, then:

`\begin{gathered} m1* m2=-1 \\ (3)/(2)* m2=-1 \\ m2=-(2)/(3) \end{gathered}`

Let:

`(x1,y1)=(2,-1)`

Using the point slope equation:

`\begin{gathered} y-y1=m2(x-x1) \\ y-(-1)=-(2)/(3)(x-2) \\ y+1=-(2)/(3)x+(4)/(3) \\ y=-(2)/(3)x+(1)/(3) \end{gathered}`