Question

What is the y-intercept of the line perpendicular to (1,1) and (-3,-1) and passes through (-3,-2)

Answer 1

Answer:

-8

Step-by-step explanation:

Let's first establish the reference line (the one that the second line will be perpendicular to).  We are told that this line passes through two points:

(1,1) and (-3,-1).

We'll find a line equation using the point slope form format to start:  

(y - y1) = m * (x - x1), where m is the slope and the x and y are from two points.

(x,y) = (1,1)

(x1,y1) = (-3,-1)

Rearrange the equation:

(y - y1) = m * (x - x1)

m = (y - y1)/ (x - x1)

m = (1-(-1))/(1-(-3))

m = 2/4, or 1/2:  The slope is 1/2.    [This is "m."]

We can use the slope-intercept form for this line (y=mx + b) and then calculate b, the y-intercept:

y = (1/2)x + b

Use either of the two given points.  I'll use (1,1) since I have memorized the "1" math tables.

y = (1/2)x + b  

1 = (1/2)(1) + b for (1,1)

b = 1/2

This makes the reference line:  y = (1/2)x+(1/2)

===

The line perpendicular must have a slope that is the negative inverse of (1/2).  This would be -(2/1), or -2.

We can then write y = -2x + b

To find be, enter the one given point for this line:  (-3,-2)

y = -2x + b

-2 = -2(-3) + b

-2 = 6 + b

b = -8

The perpendicular line is thus:

y = -2x - 8

It has a y-intercept of -8