Question

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

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

Answer 1

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

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

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 $y=\left(\frac{3}{2}\right)x+(-\frac{5}{2})⟹y=\frac{3}{2}x-\frac{5}{2}$

Hence, option B is correct.