Line k 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 and (2, 9), and (2, 0). What is the slope of line k ?

I have tried to solve it using Pythagorean theorem, so for base its 6 and for height its 9/2

So, 36+81/4 = z*z

225/4 = z*z

z= 15/2

But the correct answer is 3/4 which is achievable using slope formula. My asking is why the Pythagorean theorem not working, what am I missing here or any mistake?

Thanks

Through Pythagoras theorem, what you found was the length of the line from its x intercept to the mid point.

What is asked is the slope. Slope in other words denotes the **inclination** or **angle** (precisely tan of the angle) of the line, not it’s length.

The conventional formula for the slope is \frac{y2-y1}{x2-x1}, or just the \frac{height}{width} where height is the vertical length between two points on the line (in this case 4.5 as you have mentioned) and width is the horizontal length between the same two points on the line (in this case 6 as you have mentioned)