A line passes through (9,3),(12,4), and (n,-5) Find the value of n.

tricotasu 2020-10-26 Answered
A line passes through (9,3),(12,4), and (n,-5)
Find the value of n.
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Expert Answer

coffentw
Answered 2020-10-27 Author has 103 answers

Given that a line passes through the points (9, 3), (12, 4), and (n, -5).
First we find the equation of the line that. passes through the points (9,3), and (12,4).
The equation of a line passing through the points (x1,y1),(x2,y2) is
yy1xx1=y1y2x1x2
In this problem (x1,y1)=(9,3), and (x2,y2)=(12,4).
This implies that x1=9,y1=3,x2=12,y2=4
. Plugging these values yy1xx1=y1y2x1x2 we get the equation of the line is
yy1xx1=y1y2x1x2
y3x9=34912
y3x9=13
3(y3)=x9
3y9=x9
x3y=0
Therefore, the equation of the line is x3y=0
Also given that the line passing through the point (n,5)
Putting x=n, and y=5 in the equation of the line we get
x3y=0
n3(5)=0
n+15=0
n=15
Thus, the value of n is -15,

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