x=0，y=b
y=0，x=-b/3
S= 1/2|xy|=b^2/6= 12
b^2=72
b= 6√2
So y = 3x 6 √ 2.
(2) When the intersection of the first-order function is known (1, 2), the product of the abscissa of the intersection between the image and the X axis and the ordinate of the intersection with the Y axis is 9, and the first-order resolution function can be obtained.
Let the resolution function be once: y=kx+b intersection (1, 2).
2=k+b ①
The product of the abscissa intersecting the X axis and the ordinate intersecting the Y axis is 9.
x=0 y=b
y=0 x=-b/k
b*b=-9k ②
Solution ① ②
B=3 k=- 1 or b=6 k=-4.
The temporal resolution function:
Y=-x+3 or y=-4x+6.
③ The linear function y=ax+b and the inverse proportional function y=k/x intersect at point A and point B, and the inverse proportional function and the linear resolution function A(2, m)B(- 1, -4) are found.
Inverse function y = 4/x.
Linear function: A(2, m) is substituted into y = 4/x, and m=2, so A(2, 2).
A (2,2) b (-1,-4) is substituted into y=ax+b to obtain a set of equations, 2=2k+b and -4=-k+b,
The solution is k=2 and b=-2, so y=-2x-2.
④ the straight line PA is a linear function, y = x+n (n >); 0), the straight line PB is a linear function y =-2x+m (m >; N), point A.B is on the x axis. (1) The three-point coordinate of a.b.p is represented by m.n. (2) If Q is the focus of PA and Y axis, S- quadrilateral pqob = 6/5, and AB length is 2, then the resolution function of P-point coordinate and straight line PA. Found PB.
Point A.B is on the x axis.
A .. 0)
B(m/2，0)
Solve equation (1)(2)
y=x+n( 1)
y=-2x+m(2)
X=(m-n)/3。
y=(m+2n)/3
Point p coordinates ((m-n)/3. (m+2n)/3}
2. Because AB=2, n+m\2=2.
SPQOB=S triangle APB-S triangle AQO = 2x (m+2n) \ 3x1\ 2-nxnxx1\ 2
2x(m+2n)\ 3x 1 \ 2-NX 1 \ 2 = 6 \ 5
According to these two equations, the coordinates and analytical expressions of N. M and P points can be calculated.
⑤ It is known that the image of a linear function passes through A(2,-1) and point B, where point B is the intersection of another straight line y= 5x+3 and the Y axis, and the analytical expression of this linear function is found.
Solution: let the analytical formula of this linear function be: y = k x+b.
Get b (0,3) from the meaning of the question.
The image passes through A(2,-1) and b (0,3).
∴ 2k+b= - 1
k= -2，b=3
The resolution function is: y = -2x+3.