Question

Which of the following statement is / are correct for 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

ax + by + c = 0

a = 2, b= -3 &c = 5

y = $\frac{-a}{b}x-\frac{c}{a}$

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

Given equation can also be written in intercept form

2x - 3y + 5 = 0

2x - 3y = -5

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

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

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

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

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

Hence, all the given statements are correct.