Question

Line q goes through points (-3, 3) and (-5, -3)at what point does line q cross the y-axis?

Answer 1

Answer: At point (0,12) line q cross the y-axis.

Explanation:

Equation of a line passing through (a,b) and (c,d) :

`(y-b)=(d-b)/(c-a)(x-a)`

Given: Line q goes through points (-3, 3) and (-5, -3).

Equation of line q:

`(y-3)=(-3-3)/(-5(-(-3))(x-(-3))\\\\\Rightarrow\ (y-3)=(-6)/(-5+3)(x+3)\\\\\Rightarrow\ (y-3)=(-6)/(-2)(x+3)\\\\\Rightarrow\ y-3=3(x+3)`

When line crosses y-axis , x=0 .

So,

`y-3=3(3)\\\\\Rightarrow\ y-3=9\\\\\Rightarrow\ y=9+3\\\\\Rightarrow\ y=12`

Hence, At point (0,12) line q cross the y-axis.