A student writes $4 x = 9 - 3 y$ in the standard form as $4 x - 3 y - 9 = 0$ . What is wrong?

Class 9Linear Equations in Two VariablesLinear Equations

ANothing is wrong — $4 x - 3 y - 9 = 0$ is correct
BThe $y$ -term changes sign as it crosses over: it should be $4 x + 3 y - 9 = 0$
CThe constant changes sign: it should be $4 x - 3 y + 9 = 0$
DThe $x$ -term should be negative: it should be $- 4 x + 3 y - 9 = 0$

Step-by-Step Solution

Bringing

9 - 3 y

to the left flips BOTH signs:

4 x - 9 + 3 y = 0

, i.e.

4 x + 3 y - 9 = 0

. Check with (0, 3):

4 (0) = 9 - 3 (3) = 0

✓ and

4 (0) + 3 (3) - 9 = 0

✓, while the student’s version gives −18.

Answer: B) The

y

-term changes sign as it crosses over: it should be

4 x + 3 y - 9 = 0

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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