Given the function f(x) = - 2x + 5 calculate the area of the triangle between x,y axis and the graph of f(x)

To calculate the area of the triangle ABC, we'll have to
determine the x and y intercepts of the graph of the function f(x) = -2x +
5.

To calculate x intercept, we'll have to put y = 0. But y
= f(x).

f(x) = 0

-2x + 5 =
0

-2x = -5

x =
5/2

x = 2.5

The intercepting
point of the line -2x + 5 and x axis is B(2.5 , 0).

To
calculate y intercept, we'll have to put x = 0.

f(0) = -2*0
+ 5

f(0) = 5

The intercepting
point of the line -2x + 5 and y axis is C(0 , 5).

Since the
x axis is perpendicular to y axis, the triangle 0BC is right angled triangle and the
area is the half of the product of cathetus OB and OC.

A =
OB*OC/2

We'll calculate the lengths of the cathetus OB and
OC.

OB = sqrt[(xB-xO)^2 +
(yB-yO)^2]

OB = sqrt
[(2.5)^2]

OB = 2.5

OC =
sqrt[(xC-xO)^2 + (yC-yO)^2]

OC = sqrt
5^2

OC = 5

A =
5*2.5/2

A =
2.5^2

The area of the right angled triangle
OBC is: A = 6.25 square units.