Question

A line passing through point ($\frac{1}{2},\frac{9}{4}$), has y-intercept of 3. Find the x-intercept of the line.

• A. 0
• B. 1
• C. Not definite
• D. Insufficient data

Answer 1

The correct option is A

0

Equation of line which makes x-intercept and y-intercept at 'a' and 'b' respectively is given by

$\frac{x}{a}+\frac{y}{b}=1$
The y-intercept is 3, so 'b' = 3 and it passes through point ($\frac{1}{2},\frac{9}{4}$).

Substituting the value we get,

$\frac{1}{2a}+\frac{9}{4\times 3}=1$
$\Rightarrow \frac{1}{2a}+\frac{3}{4}=1$
$\Rightarrow \frac{1}{2a}=1-\frac{3}{4}$
$\Rightarrow \frac{1}{2a}=\frac{1}{4}$
$\Rightarrow a=2$

Hence, the x-intercept is 2.