I think the answer is
A.) infinitely many
Answer:
The equation is not linear
Step-by-step explanation:
You are given the equation
![\dfrac{2}{x}+\dfrac{y}{4}=\dfrac{3}{2}](https://tex.z-dn.net/?f=%5Cdfrac%7B2%7D%7Bx%7D%2B%5Cdfrac%7By%7D%7B4%7D%3D%5Cdfrac%7B3%7D%7B2%7D)
Express y in terms of x:
![\dfrac{y}{4}=\dfrac{3}{2}-\dfrac{2}{x}\\ \\\dfrac{y}{4}=\dfrac{3x-4}{2x}\\ \\y=4\cdot \dfrac{3x-4}{2x}\\ \\y=\dfrac{6x-8}{x}](https://tex.z-dn.net/?f=%5Cdfrac%7By%7D%7B4%7D%3D%5Cdfrac%7B3%7D%7B2%7D-%5Cdfrac%7B2%7D%7Bx%7D%5C%5C%20%5C%5C%5Cdfrac%7By%7D%7B4%7D%3D%5Cdfrac%7B3x-4%7D%7B2x%7D%5C%5C%20%5C%5Cy%3D4%5Ccdot%20%5Cdfrac%7B3x-4%7D%7B2x%7D%5C%5C%20%5C%5Cy%3D%5Cdfrac%7B6x-8%7D%7Bx%7D)
The linear function must of form
![y=mx+b,](https://tex.z-dn.net/?f=y%3Dmx%2Bb%2C)
where m and b are real numbers.
Your function is not of this form, so this is not a linear function.
Use the app Photomath it literally helps with everything and it explains
It is the distance between -14 and 0 on the number line