Question

The two lines y= 6x+15 and y= mx+4 intersect at x= -2. What is the y-coordinate of their intersection point

Answer 1

The y-coordinate of their intersection point is 3

That is y=3

Explanation:

Given two lines are y=6x+15 and y=mx+4

Given that the two lines intersect at x=-2

To find the y coordinate of their intersection point :

Equating the two lines

6x+15=mx+4

6x+15-mx-4=0

6x-mx+11=0

(6-m)x+11=0

At x=-2 (6-m)x+11=0

(6-m)(-2)+11=0

(6-m)(-2)=-11

`6-m=(11)/(2)`

`-m=(11)/(2)-6`

`-m=(11-12)/(2)`

`-m=(-1)/(2)`

`m=(1)/(2)`

Substitute the value
`m=(1)/(2)` in y=mx+4 we get

`y=(1)/(2)x+4`

At x=-2
`y=(1)/(2)(-2)+4`

`=-1+4`

`=3`

Therefore y=3

Therefore the y-coordinate of their intersection point is 3