In the figure, Blueline is Line AB and Redline is target line.
You can see that the target line does not pass through (18,-8)
Step-by-step explanation:
In the figure, Blueline is Line AB and Redline is target line.
You can see that the target line does not pass through (18,-8)
Taking a bottom-left corner of the graph as (0,0)
Given Line AB,
Point A is located as (4,9)
Point B is located as (16,1)
The slope of AB is
[tex]=\frac{Y1-Y2}{X1-X2}[/tex]
[tex]=\frac{9-1}{4-16}[/tex]
[tex]=\frac{8}{-12}[/tex]
[tex]=\frac{-2}{3}[/tex]
The question says " Draw a line passes through C(13,12) and parallel to Line AB "
Now, Let the equation of the target line is y=mx + c
Where m=slope and c is the y-intercept
The target line is parallel to the line AB
The slope of the Target line = The slope of the Line AB [tex]=\frac{-2}{3}[/tex]
m=[tex]=\frac{-2}{3}[/tex]
We can write, the equation of the target line is
[tex]y=\frac{-2}{3}x + c[/tex]
Also, the Target line is passing through C(13,12)
Point C satisfies the equation
[tex]y=\frac{-2}{3}x + c[/tex]
[tex]12=\frac{-2}{3}13 + c[/tex]
[tex]12=\frac{-26}{3} + c[/tex]
[tex]12+\frac{26}{3}=c[/tex]
[tex]c= 12+\frac{26}{3}[/tex]
[tex]c= \frac{62}{3}[/tex]
Replacing the value
the equation of the target line is
[tex]y=\frac{-2}{3}x + c[/tex]
[tex]y=\frac{-2}{3}x + \frac{62}{3} [/tex]
[tex]3y= -2x + 62 [/tex]
It is also asked that if a line is extended , would it passes through the (18,-8)?
If a line passes through the point (18-,8) then, that point must satisfy the equation of a line
the equation of the target line is [tex]3y= -2x + 62 [/tex]
[tex]3(-8)= -2(18) + 62 [/tex]
[tex](-24)= (-36) + 62 [/tex]
[tex](-24)= (-36) + 62 [/tex]
[tex](-24)= 26 [/tex]
Left land side is not equal to right hand side.
Therefore. a line does not pass through the point (18,-8)
