Question

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

$\frac{x}{4}+\frac{y}{3}=2$

• A. $y=\frac{3}{4}x+6$
• B. $4y=-3x-24$
• C. $y=-\frac{3}{4}x+6$
• D. $4y=-\frac{3}{4}x+6$

Answer 1

The correct option is C $y=-\frac{3}{4}x+6$

The given equation is $\frac{x}{4}+\frac{y}{3}=2$ ........... $\left(i\right)$

Now, an equation of line of any form can be represented in slope-intercept form by solving the equation for $y$.

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

$\therefore \frac{x}{4}+\frac{y}{3}=2⟹3x+4y=24⟹y=-\frac{3}{4}x+6$ which is in the form of $y=mx+c$.

Hence, option C is correct.