How to write the eighth and ninth questions on page 1 120 of the eighth grade people's education edition mathematics book?

Question 8: Because the image of the function is a straight line passing through the origin.

Let the analytical expression of the function be y=kx.

Because it passes point (2, -3a), it is: -3a=k*2, and a=-2k/3 (1) is obtained.

If it passes through point (a, -6), then: -6=k*a (2)

Substituting (1) into (2) gives -6 = k *(2k/3).

Finishing: k? =9 k= 3

And because the straight line passes through the fourth quadrant, k < 0 means k=-3.

Therefore, the analytical expression of this function is y=-3x.

Question 9

1) If P is the intersection of PC⊥X axis and C is the intersection of X axis, then PC = YOC = X.

s = 1/2 * OA * PC = 1/2 * 6 * y = 3y

X+y=8 so: S=3*(8-x)=24-3x.

24-3x > 0 0 < x < 8, because s > 0.

2) When the abscissa of point P is 5, that is, x=5.

△△OPA area S=24-3*5=9

3) The area of△ OPA should not be greater than 24.

Because the area of △OPA is s = 24-3x0 < x < 8.

So the area s is 0.