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

The given straight line is 2x - 3y + 5 = 0.

Comparing given line with general form of a straight line : ax + by + c = 0,

we get, a = 2, b= -3 & c = 5.

Now, y = $\left(\frac{-a}{b}\right)x-\frac{c}{b}$

So, the slope is $\frac{-a}{b}=\frac{-2}{-3}=\frac{2}{3}$

The given equation can also be written in the intercept form as:

2x - 3y + 5 = 0

$\to 2x-3y=-5\to \frac{2x}{-5}-\frac{3y}{-5}=1\to \frac{x}{\left(\frac{-5}{2}\right)}+\frac{y}{\left(\frac{5}{3}\right)}=1$

Comparing this equation with $\frac{x}{a}+\frac{y}{b}=1$, we get:
X- intercept = $\frac{-5}{2}$
Y- intercept = $\frac{5}{3}$
Hence, all the given statements are correct.