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: $\dfrac{3}{4}$

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 $(\dfrac{a+c}{2},\dfrac{b+d}{2})$.

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

$(\dfrac{2+2}{2},\dfrac{9+0}{2})=(2,4.5)$

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

$m=\dfrac{s-q}{r-p}$

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

$m=\dfrac{4.5-0}{2-(-4)}=\dfrac{4.5}{2+4}=\dfrac{4.5}{6}\\\\=\dfrac{45}{60}=\dfrac{3}{4}$

Hence, the slope of line k $=\dfrac{3}{4}$