If a line that passes through the origin also passes through the points that can be denoted as (3k,k), then what is the equation of the line. Also find the point whose abscissa is 6. [4 MARKS]

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Solution

Interpretation : 1 Mark
Equation of line : 1 Mark
Calculation : 1 Mark
Result : 1 Mark

Putting k = 0, we find that the line passes through the origin (0, 0).
Thus, it is of the form y = mx [when line passes through origin its intercept on x and y axis is zero]

To find m, let’s put the point (3k, k) into the equation.
$k = m (3 k)$
$m = \frac{1}{3}$
$y = \frac{1}{3} x$
$o r x = 3 y (Equation of the line)$
Putting x = 6, we get y = 2

Thus, the required point with abscissa = 6, is (6, 2)

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