Question

Find the area of the region bounded by the y-axis, x-axis and the line y=−2x+4. You have 2 attempts left to earn the full credit for this problem. Answer: The area of the region is square units.

Answer 1

its 4

Explanation:

i know from RSM

Answer 2

Area of the bounded region = 4 sq units

Explanation:

The region bounded by y-axis,x-axis and the given line is in the shape of a right-angled triangle which is right-angled at origin.

Hence :

Area of the bounded region = Area of the right-triangle formed

=
`(1)/(2)* base* height`

Base length of the Δ = x-intercept of the line

Height of the Δ = y-intercept of the line.

x-intercept is obtained by putting y=0 in the equation y=-2x+4

∴x-intercept = 2

y-intercept is obtained by putting x=0 in the equation y=-2x+4

∴y-intercept = 4

Area of the right-triangle =
`(1)/(2)* x-intercept* y-intercept = (1)/(2)*2*4=4\ sq\ units`