Question

Which of the following statements is/are correct for the equation $2x-3y+5=0$

1. Slope of the straight line is $\frac{2}{3}$

2. x-intercept of the straight line is $\frac{-5}{2}$

3. y-intercept of the straight line is $\frac{5}{3}$

• A. only 1 & 2
• B. only 2&3
• C. only 3&1
• D. All 1, 2 & 3

Answer 1

The correct option is D

All 1, 2 & 3

Given straight line is $2x-3y+5=0$

Comparing given line with general from of line

$\Rightarrow ax+by+c=0$

$\Rightarrow a=2,b=-3andc=5$

$\Rightarrow y=\frac{-a}{b}\times -\frac{c}{a}$

Slope is $\frac{-a}{b}=\frac{-2}{-3}=\frac{2}{3}$

Given equation can also be written in intercept form

$\Rightarrow 2x-3y+5=0$

$\Rightarrow 2x-3y=-5$

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

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

Comparing this equation with $\frac{x}{a}+\frac{y}{b}=1$

$\text{X- intercept}=\frac{-5}{2}$

$\text{Y- intercept}=\frac{5}{3}$

All 1,2 and 3 statements are correct.