When $3 y = 5 x$ is written in the standard form ax + by + $c = 0$ , what are a, b and $c$ ?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

3 y = 5 x

→ bring everything to one side:

5 x - 3 y = 0

, i.e.

5 x + (- 3) y + 0 = 0

. So

a = 5, b = - 3, c = 0

. There is no constant term, so

c = 0

Answer: A)

a = 5, b = - 3, c = 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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