Answer: [tex]\dfrac{3}{4}[/tex]
Step-by-step 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 [tex](\dfrac{a+c}{2},\dfrac{b+d}{2})[/tex].
Then, the midpoint of the line segment whose endpoints are (2, 9) and (2, 0) will be :-
[tex](\dfrac{2+2}{2},\dfrac{9+0}{2})=(2,4.5)[/tex]
The slope of line passing through (p,q) and (r,s) will be :-
[tex]m=\dfrac{s-q}{r-p}[/tex]
Then, the slope of line passing through (-4,0) and (2,4.5) will be :-
[tex]m=\dfrac{4.5-0}{2-(-4)}=\dfrac{4.5}{2+4}=\dfrac{4.5}{6}\\\\=\dfrac{45}{60}=\dfrac{3}{4}[/tex]
Hence, the slope of line k [tex]=\dfrac{3}{4}[/tex]
