A line l is parallel to the y-axis and passes through the point (2,3). What is its gradient (m) and x-intercept? a. m= 0 , x= (3,0) b. m= ∞ , x= (2,0) c. m= 0 , x= (2,0) d. m= ∞ , x= (3,0) e. m= 2 , x= (0,0)
Question
A line l is parallel to the y-axis and passes through the point (2,3). What is its gradient (m) and x-intercept? a. m= 0 , x= (3,0) b. m= ∞ , x= (2,0) c. m= 0 , x= (2,0) d. m= ∞ , x= (3,0) e. m= 2 , x= (0,0)
Solution
A line parallel to the y-axis is a vertical line. The slope or gradient (m) of a vertical line is undefined or can be considered as infinity (∞).
The x-intercept of a line is the point at which the line crosses the x-axis. Since a vertical line doesn't slope, it doesn't cross the x-axis at any point other than its own. Therefore, for a line parallel to the y-axis and passing through the point (2,3), the x-intercept is at x=2 (or the point (2,0)).
So, the correct answer is b. m= ∞ , x= (2,0).
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