The intercept ratio of line L on x-axis and y-axis is 1:3, and it passes through points a (m, m-1) and B (2,3 + m) to find the value of M and the linear equation

Let the linear equation be y = KX + B
Substituting a (m, m-1) and B (2,3 + m) into
m-1=km+b
3+m=2k+b
Solution
k=4/(2-m)
b=-(m^2+m+2)/(2-m)
The linear equation is y = 4x / (2-m) - (m ^ 2 + m + 2) / (2-m)
The intercept ratio of line L on x-axis and y-axis is 1:3
So (m ^ 2 + m + 2) / 4: (m ^ 2 + m + 2) / (2-m) = 1:3
3/4=1/(2-m)
6-3m=4
m=2/3
The linear equation is y = 4x / (2-2 / 3) - [(2 / 3) ^ 2 + 2 / 3 + 2] / (2-2 / 3)
=3x-7/3
That is 9x-3y-7 = 0

It is known that the image of the first-order function Y1 = 3x-2k intersects the image of the inverse scale function y2 = k − 3x, and the ordinate of one of the intersections is 6. (1) find the analytic expressions of the two functions; (2) find the value range of X when Y1 < Y2 by combining with the image

(1) Let the intersection a (m, 6) have 3M − 2K = 6K − 3M = 6 ｛ M = − 43K = − 5 ｛ Y1 = 3x + 10, y2 = − 8x; (2) from the equations 3x + 10 = y − 8x = y, we get 3x2 + 10x + 8 = 0x1 = - 2, X2 = − 43. From the image, we can see that when x ＜ - 2 or − 43 ＜ x ＜ 0, Y1 ＜ Y2

When m is in what range, the intersection of y = 3x + M-1 and y = 2x-3m + 2 is in the third quadrant

The intersection point x = 3-2m can be calculated by linear equation
y=8-5m
The intersection point should be in the third m quadrant. X

If the function y = (m-1) x to the second power of M + 3 is a first-order function, what is the value of m when the intersection of the line y = 3x + M-1 and y = 2x-3m + 2 is in the third quadrant?

∵ y = (m-1) x ^ (m ^ 2) + 3 is a linear function
The value of M is ± 1
The intersection of y = 3x + M-1 and y = 2x-3m + 2 is in the third quadrant
∴m=-1

The intercept ratio of line L on x-axis and y-axis is 1:3, and it passes through points a (m, m-1) and B (2,3 + m) to find the value of M and the linear equation