The lines $x = 2$ and $y = 2$ are drawn on the same graph paper. Which statement is true?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

x = 2

is vertical (parallel to the

y

-axis) and

y = 2

is horizontal (parallel to the

x

-axis), so they are perpendicular and meet where

x = 2

and

y = 2

— the point (2, 2).

Answer: A) They cross at the point (2, 2)

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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