1.已知直線L:y=4x,直線M:2x+3y=-12,則L,M和y軸所圍成三角形的面積為多少平方單位?

The y-intercept of L is: when x = 0, y = 4 * 0 then, y = 0
The y-intercept of M is: when x=0, 2 (0) + 3y = -12 then, y = -4

Therefore the length between these two points is 4, which can be used as the Base for calculating the area of the triangle.

We then solve the two linear functions and the intercept point is the Apex of the triangle. The x coordinate represents the "prependicular distance to the Y-axis'', which can also be viewed as the Height of the triangle.

substitue y = x into M:
2x + 3 (4x) = -12
x = - 6 / 7 (Height is 6/7)

So, the area of the triangle is:
A = 0.5 * B * H
= 0.5 * (4) * (6/7)
= 12 / 7