Question

Line&lies in the xy-plane. The x-intercept of line K is -4, and line k passes through the midpoint of the line segment whose endpoints are (2, 9) and (2, 0). What is the slope of line k? Give your answer as a fraction

Answer 1

Answer:
`(3)/(4)`

Explanation:

Given : Line k lies in the xy-plane.

The x-intercept of line K is -4. i.e. line k is intersecting the x-axis at (-4,0).

We know that the mid point of a line passing through any two points (a,b) and (c,d) is
`((a+c)/(2),(b+d)/(2))`.

Then, the midpoint of the line segment whose endpoints are (2, 9) and (2, 0) will be :-

`((2+2)/(2),(9+0)/(2))=(2,4.5)`

The slope of line passing through (p,q) and (r,s) will be :-

`m=(s-q)/(r-p)`

Then, the slope of line passing through (-4,0) and (2,4.5) will be :-

`m=(4.5-0)/(2-(-4))=(4.5)/(2+4)=(4.5)/(6)\\\\=(45)/(60)=(3)/(4)`

Hence, the slope of line k
`=(3)/(4)`