Question

Which of the following represents the equation of the line making an intercept of 3 unit with the positive x-axis and passing through the point (2,1)?

• A. y + x + 3 = 0
• B. y - x - 3 = 0
• C. y - x + 3 = 0
• D. y + x - 3 = 0

Answer 1

The correct option is D y + x - 3 = 0

The line makes an intercept of 3 unit on positive x-axis, so it passes through the point (3,0)
The line also passes through point (2,1)

Equation of a line passing through point ($x_1,y_1$)and ($x_2,y_2$) is given by

$y-y_1$ = $\frac{y_2-y_1}{x_2-x_1}(x-x_{!})$

Substituting the value we get

$y-0$ = $\frac{1-0}{2-3}(x-3)$
$\Rightarrow$ $y-0$ = $\frac{1}{-1}(x-3)$
$\Rightarrow$ $y-0$ = -1 (x-3)
$\Rightarrow$ $y-0=-1(x-3)$
$\Rightarrow$ $y-0=-x+3$
$\Rightarrow$ $y+x-3=0$