Question

Need help with this math problem

Answer 1

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)

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

`=(Y1-Y2)/(X1-X2)`

`=(9-1)/(4-16)`

`=(8)/(-12)`

`=(-2)/(3)`

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
`=(-2)/(3)`

m=
`=(-2)/(3)`

We can write, the equation of the target line is

`y=(-2)/(3)x + c`

Also, the Target line is passing through C(13,12)

Point C satisfies the equation

`y=(-2)/(3)x + c`

`12=(-2)/(3)13 + c`

`12=(-26)/(3) + c`

`12+(26)/(3)=c`

`c= 12+(26)/(3)`

`c= (62)/(3)`

Replacing the value

the equation of the target line is

`y=(-2)/(3)x + c`

`y=(-2)/(3)x +  (62)/(3)`

`3y= -2x + 62`

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
`3y= -2x + 62`

`3(-8)= -2(18) + 62`

`(-24)= (-36) + 62`

`(-24)= (-36) + 62`

`(-24)= 26`

Left land side is not equal to right hand side.

Therefore. a line does not pass through the point (18,-8)