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

Answer:

Area of the bounded region = 4 sq units

Step-by-step 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

                                                 =$\frac{1}{2}\times base\times height$

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 = $\frac{1}{2}\times x-intercept\times y-intercept = \frac{1}{2}\times2\times4=4\ sq\ units$