The line $3 x - 2 y = 6$ is drawn. What is the area of the shaded triangle it makes with the two axes?

Class 9Linear Equations in Two VariablesLinear Equations

Step-by-Step Solution

The line cuts the

x

-axis at

(2, 0)

and the

y

-axis at

(0, - 3)

. The right triangle has legs 2 and 3, so area

= \frac{1}{2} \times 2 \times 3 = 3

sq units.

Answer: A) 3 sq units

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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