Question

Draw the graph of 3x + 2y = 6. Use the graph drawn to find the area of triangle formed by the line drawn and the co-ordinate axes.

Answer 1

Given:

Equation of the line is 3x + 2y = 6

Formula:

y = \[\frac{6 - 3x}{2}\] and Area of triangle = \[\frac{1}{2} \times \text{Base} \times \text{Height}\]

Solution:

3(0) + 2y = 6 ⇒ 2y = 6 ⇒ y = 3  [Calculating y-intercept at x = 0 to get point (0, 3)]

3x + 2(0) = 6 ⇒ 3x = 6 ⇒ x = 2  [Calculating x-intercept at y = 0 to get point (2, 0)]

∴ Base of triangle = 2 units  [Distance between Origin (0, 0) and x-intercept (2, 0)]

∴ Height of triangle = 3 units  [Distance between Origin (0, 0) and y-intercept (0, 3)]

\[\therefore \text{Area of triangle} = \frac{1}{2} \times 2 \times 3 = 3 \text{ sq. units} \quad [\text{Calculating the area using the formula}]\]

∴ 3 sq. units