Question

The $x$ and $y$ intercepts of the following line is:

$3y-2x+5=0$

• A. $a=\frac{2}{5},b=-\frac{3}{5}$
• B. $a=\frac{5}{2},b=\frac{5}{3}$
• C. $a=\frac{2}{5},b=\frac{3}{5}$
• D. $a=\frac{5}{2},b=-\frac{5}{3}$

Answer 1

The correct option is D $a=\frac{5}{2},b=-\frac{5}{3}$

Given- The equation of a line is $3y-2x+5=0$

To find out- the equation of the line in intercept form which is $\frac{x}{a}+\frac{y}{b}=1$ when $a=x$-intercept and $b=y$-intercept.

Solution-

$3y-2x+5=0$

$\Rightarrow 2x-3y=5$

Dividing both sides by $5$, we get

$\frac{2x}{5}-\frac{3y}{5}=1$

$\Rightarrow \frac{x}{\frac{5}{2}}+\frac{y}{-\frac{5}{3}}=1$

Therefore, $x$-intercept $=a=\frac{5}{2}$, $y$-intercept $=b=-\frac{5}{3}$.