Question

y = 4x is the equation of a line which passes through,
(a) y-axis (b) positive x-axis (c) origin (d) negative x-axis​

Answer 1

$\underline{\textsf{Given:}}$

$\textsf{Equation of the line is y=4x}$

$\underline{\textsf{To find:}}$

$\textsf{whether the given line passes through origin}$

$\underline{\textsf{Solution:}}$

$\textsf{Consider,}$

$\textsf{Put x=0 and y=0}$

$\mathsf{0=4(0)}$

$\mathsf{0=0}$

$\textsf{The equation is satisfied}$

$\textsf{The given line passes through (0,0)}$

$\textsf{Also, the equation is of the form y=mx}$

$\textsf{It does not passes through x axis or y axis}$

$\underline{\textsf{Answer:}}$

$\textsf{Option(c) is correct}$

Answer 2

SOLUTION :

TO CHOOSE THE CORRECT OPTION

y = 4x is the equation of a line which passes through

(a) y-axis

(b) positive x-axis

(c) origin

(d) negative x-axis

CONCEPT TO BE IMPLEMENTED

The general equation of any line is

$\sf{}ax + by = c \: \: \: \: ..(1)$

If the line passing through origin that is (0,0)

Then putting x = 0 & y = 0 in Equation (1) we get

$\sf{}0 + 0 = c$

$\implies \sf{}c = 0$

Thus equation (1) reduces to

$\sf{}ax + by = 0$

Thus in conclusion we can state that, the general equation of any line passing through origin is of the form

$\sf{}ax + by = 0$

EVALUATION

The given equation of the line is

$\sf{}y = 4x$

$\sf{}4x - y = 0$

Comparing with

$\sf{}ax + by = c \: \: \: we \: \: get$

$\sf{}a= 4, b = - 1, c = 0$

Since c = 0

So the line passes through origin

FINAL ANSWER

y = 4x is the equation of a line which passes through

(c) origin

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