Question

The equation of the line whose slope is $ 3 $ and which cuts off an intercept of $ 3 $ units from the positive x axis is:
(A) $ y = 3x - 9 $
(B) $ y = 3x + 3 $
(C) $ y = 3x + 9 $
(D) None of these

Answer 1

Hint: In the given problem, we are required to find the equation of a line whose slope is given to us and cuts off an intercept on the positive x axis as provided to us. We can easily find the equation of the line using the slope point form of a straight line. So, we first substitute the value of slope given to us and then substitute the coordinates of point given to us as positive x intercept of the straight line.

Complete step-by-step answer:
So, the slope of line \[ = m = 3\]
Also, we are given that the line cuts off an intercept of three units on the positive axis.
So, the point \[\left( {3,0} \right)\] lies on the required straight line.
Now, we know the slope point form of the line, where we can find the equation of a straight line given the slope of the line and the point lying on it. The slope point form of the line can be represented as: $ \left( {y - {y_1}} \right) = m\left( {x - {x_1}} \right) $ where $ \left( {{x_1},{y_1}} \right) $ is the point lying on the line given to us and m is the slope of the required straight line.
Considering $ {x_1} = 3 $ and $ {y_1} = 0 $ as the point given to us is \[\left( {3,0} \right)\]
Therefore, required equation of line is as follows:
 $ (y - 0) = 3(x - 3) $
On opening the brackets and simplifying further, we get,
 $ \Rightarrow y = 3x - 9 $
Hence, the equation of the straight line is: $ y = 3x - 9 $ .
Therefore, option (A) is the correct answer.
So, the correct answer is “Option A”.

Note: The given problem requires us to have thorough knowledge of the concepts of coordinate geometry. The equation of the straight line in all the forms must be remembered. The applications of concepts learnt in coordinate geometry are wide ranging. We should know that the y coordinate of any point lying on the x axis is always zero.