Which description fits ALL the solutions of the equation $4 x + 0 \cdot y = 12$ ?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

4 x = 12

→

x = 3

. Because

y

is multiplied by 0 it is free, so (3, 0), (3, 7), (3, −2) … all work. Together they form the vertical line

x = 3

Answer: B)

x = 3

, while

y

may be any real number

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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