What is the area bounded by the line 𝑥+2𝑦=4 and the two axes in the Cartesian plane?

Step 1: Rewrite the equation in slope-intercept form (y = mx + b)

x + 2y = 4 can be rewritten as y = -1/2x + 2

Step 2: Identify the x and y intercepts

The x-intercept is the value of x when y = 0. Setting y = 0 in the equation gives x = 4.

The y-intercept is the value of y when x = 0. Setting x = 0 in the equation gives y = 2.

Step 3: Sketch the line and the intercepts on the Cartesian plane

The line crosses the x-axis at x = 4 and the y-axis at y = 2. The area bounded by the line and the axes forms a triangle.

Step 4: Calculate the area of the triangle

The area of a triangle is given by the formula 1/2 * base * height. Here, the base is the x-intercept (4) and the height is the y-intercept (2).

So, the area of the triangle is 1/2 * 4 * 2 = 4 square units.