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What is the area of the triangle formed by the coordinate axes and the line​2x+3y=62x+3y=62x+3y=6 ?​
Question

What is the area of the triangle formed by the coordinate axes and the line

2x+3y=62x+3y=6 ?​

A.

3 sq. units

B.

2 sq. units

C.

12 sq. units

D.

6 sq. units

Correct option is A

Given:

Line: 2x + 3y = 6

Formula Used:

Area of triangle =12×x-intercept×y-intercept \frac{1}{2} \times \text{x-intercept} \times \text{y-intercept}

Solution:
Find x-intercept:

Set y = 0:

2x = 6

x = 3

Find y-intercept:
Set x = 0:

3y = 6

y = 2

Area =12×3×2=3 square units= \frac{1}{2} \times 3 \times 2 = 3 \text{ square units}

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