It is known that, as shown in the figure, the image of the linear function y = KX + B (K ≠ 0) passes through points a (0,3), B (4,6) 1) Finding the analytic expression of a function 2) Point P is a moving point on a linear function. Take P as the center of the circle and 5 as the radius to make a circle. If the length of the line segment cut by the circle P on the x-axis is 6, the coordinates of point P can be obtained Speed~

It is known that, as shown in the figure, the image of the linear function y = KX + B (K ≠ 0) passes through points a (0,3), B (4,6) 1) Finding the analytic expression of a function 2) Point P is a moving point on a linear function. Take P as the center of the circle and 5 as the radius to make a circle. If the length of the line segment cut by the circle P on the x-axis is 6, the coordinates of point P can be obtained Speed~

(1) Given that the image of the first-order function y = KX + B (K ≠ 0) passes through points a (0,3), B (4,6), then substituting the coordinates of points a and B into the analytic expression of the function respectively, we can get the following results:
{ b=3
{ 4k+b=6
It is easy to get: B = 3, k = 3 / 4
So the analytic formula of a function is y = 3x + 3
(2) From (1), let the P coordinate of the moving point on the straight line of the linear function be (m, 3m / 4 + 3),
Then the distance from point P to X axis is 3 M + 3
The radius of the circle with P as the center is 5, and the length of the line segment cut by the circle P on the x-axis is 6,
Therefore, according to the vertical diameter theorem:
(3m / 4 + 3) &# 178; + 3 & # 178; = 5 & # 178;
That is (3m / 4 + 3) &# 178; = 16
The result is: 3m / 4 + 3 = 4 or 3m / 4 + 3 = - 4
The solution is: M = 4 / 3 or M = - 28 / 3
So the point P coordinates are (4 / 3,4) or (- 28 / 3, - 4)

If the image with positive scale function y = KX passes through the point (- 1,0.5), then K=

Substituting the point (- 1,0.5), we get
0.5=-k
k=-0.5