Indicate the equation of the given line in standard form. The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).

Question

Indicate the equation of the given line in standard form.

The line through the midpoint of and perpendicular to the segment joining points (1, 0) and (5, -2).

Answer 1

Standard form of a linear equation is Ax+By=C.

 

To write the equation, first we need to know the slope and a point.

 

1. Find Slope

 

Our slope is perpendicular to the that of the points given, so we need to find their slope, and then take the negative reciprocal.

 

Using their points (1,0) and (5,-2), the slope is:

(Δy)/(Δx)=(-2)/(+4)=-1/2.

 

Therefore, OUR slope is 2/1=2.

 

2. Find a Point

 

Our line must contain the midpoint of (1,0) and (5,-2), so that is the point I want.  The midpoint is the (average x, average y)=(3,-1).

 

3. Write an Equation

 

We can use slope-intercept (have to find the y-intercept) or just substitute into point-slope form.

m=2

(3,-1)

 

y-y₁=m(x-x₁)

 

Substitute values:

y-(-1)=(2)(x-(3))

 

Simplify and rewrite in Standard Form:

y+1=2x-6
-2x+1y=-7

 

Note: many texts don't want the leading coefficient to be negative, so you might have to multiply everything by (-1)

2x-1y=7