Question

Represent the given equation in $y=mx+c$ form :

$\frac{x}{2}+\frac{y}{3}=1$

• A. $y=-\frac{3}{2}x+3$
• B. $y=\frac{3}{2}x+3$
• C. $y=-\frac{3}{2}x-3$
• D. $y=\frac{3}{2}x-3$

Answer 1

The correct option is A $y=-\frac{3}{2}x+3$

The given equation is $\frac{x}{2}+\frac{y}{3}=1$ ........... $\left(i\right)$

Now, the equation of a line of any form can be converted into slope-intercept form by solving the equation for $y$

Let's solve $\left(i\right)$ for y,

$\therefore \frac{x}{2}+\frac{y}{3}=1⟹3x+2y=6⟹y=-\frac{3}{2}x+3$ which is in the form of $y=mx+c$.

Hence, option A is correct.