Question

The area of the triangle formed with the X-Axis, Y-Axis and the line
representing the equation x + y = 6 is​

Answer 1

Answer:

The x and y axes automatically become the height and base of the triangle. The diagonal line 3x - y - 6 = 0 will determine what lengths they have.

To do this, we need to put it in y = mx + b format:

3x−y−6=0

3x−y=6

−y=6−3x

y=3x−6

It crosses the y -axis at:

y=3x−6

y=3(0)−6

y=0−6

x = 2

(0, -6)

It crosses the x-axis at:

y=3x−6

0=3x−6

6=3x

x = 2

(2, 0)

So we have a triangle with a base of 2 units and a height of | - 6| = 6 units. We can now find the area:

A=12bh

A=12(2)(6)

A=6 square units