Question

Find the equation of straight line which passes through the point 4,-2 and whose intercept on y axis is twice that on x axis

Answer 1

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Answer 2

The equation would be y = -x + 2

Step-by-step explanation:

Let x intercept of the line is a,

Then y-intercept of the line is 2a

So, line passes through (a, 0) and (0, 2a),

We know that,

Equation of a line passes through $(x_1, y_1)$ and $(x_2, y_2)$ is,

$y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

Thus, the equation of the line is,

$y - 0 = \frac{2a}{-a}(x-a)$

$y=-1(x-a)$

y = -x + a

Since, line passes through the point (4, -2),

i.e. (4, -2) will be satisfy the equation of line.

-2 = -4 + a

⇒ a = -2 + 4 = 2

Hence, the required equation of the line is,

y = -x + 2

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