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 the given line with general from of line

ax + by + c = 0, a = 2, b= -3 &c = 5

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

The 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 = $\frac{5}{3}$

All the statements are correct.