Which of these equations does NOT represent a line parallel to one of the axes?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

y + 4 = 0

y = - 4

(horizontal),

3 x = 9

x = 3

(vertical) and

y = 7

is horizontal. Only

2 x + y = 5

keeps both variables, so it is a slanting line — it passes through (0, 5) and (1, 3).

Answer: D)

2 x + y = 5

Two special cases:

**

y

= constant**: a horizontal line (parallel to

x

-axis). Example:

y = 4

is the line of all points with ordinate 4. Every solution has

y = 4

regardless of

x . * * x

= constant**: a vertical line (parallel to

y

-axis). Example:

x = - 2

is the line of all points with abscissa −2.

Algebraically:

y = 4

0 x + y - 4 = 0

;

x = - 2

x + 0 y + 2 = 0

. They fit the standard form ax + by +

c = 0

with one of a, b being 0.

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