Question

A-യുടെ Y-കോർഡിനേറ്റ് 3-ഉം, B-യുടെ X-കോർഡിനേറ്റ് 2-ഉം ആകുന്നു. എങ്കിൽ AB എന്ന വരയുടെ സമവാക്യം എന്താണ്?

• A. 3x+2y=6
• B. 3x-2y=6
• C. 2y=3x+6
• D. 2y-3x=6

Answer 1

Answer:

B. 3x-2y=6

Based on the provided image and description, the equation of the line AB is $3x - 2y = 6$.

1. Find the coordinates of points A and B:

   • Point $B$ lies on the positive X-axis with an X-coordinate of $2$. Therefore, its coordinates are $(2, 0)$.

   • Point $A$ lies on the negative Y-axis with a distance of $3$ units below the origin. Therefore, its coordinates are $(0, -3)$.

2. Use the Intercept Form of a line:
   The intercept form equation is given by:
   $\frac{x}{a} + \frac{y}{b} = 1$
   Where:

   • $a$ is the X-intercept = $2$

   • $b$ is the Y-intercept = $-3$

3. Substitute the values and simplify:
   $\frac{x}{2} + \frac{y}{-3} = 1$
   $\frac{x}{2} - \frac{y}{3} = 1$ Taking the Least Common Multiple (LCM = 6) to eliminate fractions:
   $\frac{3x - 2y}{6} = 1$
   $3x - 2y = 6$