Question

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

• A. (A) -2
• B. (B) 2
• C. (C) 23
• D. (D) −23

Answer 1

Answer: (A)

(A) -2

Answer 2

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−y1=m(x−x1)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 −1m.Given,3x+y=7⇒y=−3x+7Then the slope of a line perpendicularThe slope of line =m=−3Then the slope of a line perpendicular to it is −1m=13The equation of line passing through (1,1) with slope 13 is,y−1=(13)(x−1)⇒3y−3=x−1⇒3y=x+2⇒3y−x=2For x-intercept, y=0∴x=−2So, the x-intercept of line is −2Hence, the correct option is (A).