Question

The equation of the line $2y-3x+5=0$ in slope-intercept form is

• A. $y=\frac{2}{3}x+\frac{2}{5}$
• B. $x=\frac{2}{3}y+\frac{5}{2}$
• C. $y=\frac{3}{2}x-\frac{5}{2}$
• D. $y=-\frac{2}{3}y+\frac{5}{2}$

Answer 1

The correct option is C $y=\frac{3}{2}x-\frac{5}{2}$

The given equation of line is $2y-3x+5=0$ or $-3x+2y+5=0$ ..... $\left(1\right)$

Now, an equation $ax+by+d=0$ ..... $\left(2\right)$ can be written in slope-intercept form i.e

in the form $y=mx+c$ by solving the equation for $y$.

So the slope-intercept form of the equation $ax+by+d=0$ is

$y=(-\frac{a}{b})x+(-\frac{d}{b})$ i.e $m=(-\frac{a}{b})$ and $c=(-\frac{d}{b})$

Here $a=-3,b=2$ and $d=5$ ......... By comparing $\left(1\right)$ and $\left(2\right)$

$\therefore m=(-\frac{(-3)}{2})$ and $c=(-\frac{5}{2})$ from $\left(1\right)$

$\therefore$ The slope-intercept form of the given equation is $y=(-\frac{-3}{2})x+(-\frac{5}{2})⟹y=\frac{3}{2}x-\frac{5}{2}$

Hence, option C is correct.