Given:
\(\frac{x}{a}\) + \(\frac{y}{b}\) = 1
The given linear equation is in the slope intercept form. Intercept means the distance at which the given equation cuts or meets the coordinate axis. In this problem a & b are the intercepts on the x and y axis respectively.
The triangle formed by a straight line with the coordinate axis is a right angled triangle where the angle subtended at origin is 90°. So the length of the x intercepts becomes the perpendicular and y intercept becomes the base of the triangle.
We know,
Area Of a triangle = \(\frac{1}{2}\) x (perpendicular length) x (base length)
So,
Area of the triangle becomes \(\frac{1}{2}\)ab
The Area of the triangle is \(\frac{1}{2}\)ab
