Question

A line passes through $(1,1)$ and is perpendicular to the line $3x+y=7$. Its $x$-intercept is:

• (A) -2
• (B) 2
• (C) $\frac{2}{3}$
• (D) $\frac{-2}{3}$

Answer 1

The Correct Option is A

Explanation:
Concept:Slope intercept form of line: y = mx + c, Where ‘m’ is the slope of the line and ‘c’ is the y-intercept.The "point-slope" form of the equation of a straight line is: $y-y_1=m(x-x_1)$When two lines are perpendicular, the product of their slope is -1.If m is the slope of a line, then the slope of a line perpendicular to it is $-\frac{1}{m}$.Given,$3x+y=7$$\Rightarrow y=-3x+7$Then the slope of a line perpendicularThe slope of line $=m=-3$Then the slope of a line perpendicular to it is $\frac{-1}{m}=\frac{1}{3}$The equation of line passing through $(1,1)$ with slope $\frac{1}{3}$ is,$y-1=(\frac{1}{3})(x-1)$$\Rightarrow 3y-3=x-1$$\Rightarrow 3y=x+2$$\Rightarrow 3y-x=2$For $x$-intercept, $y=0$$\therefore x=-2$So, the x-intercept of line is $-2$Hence, the correct option is (A).