What is the yintercept of the line perpendicular to (1,1) and (3,1) and passes through (3,2) The yintercept is
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The yintercept is
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1. User Answers rspill6
Answer:
8
Stepbystep 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 slopeintercept form for this line (y=mx + b) and then calculate b, the yintercept:
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 yintercept of 8