We know that the image of the first-order function passes through the point P (2,3), and the image and the y-axis intersect at the point m, and the distance from the point m to the origin is equal to 5. Find the expression of the first-order function and draw the qualified image

We know that the image of the first-order function passes through the point P (2,3), and the image and the y-axis intersect at the point m, and the distance from the point m to the origin is equal to 5. Find the expression of the first-order function and draw the qualified image

∵ the graph of a linear function intersects with the Y axis at point m, and the distance from point m to the origin is equal to 5,
The coordinates of point m are (0,5) or (0, - 5)
When the point m coordinate is (0,5), let the first-order function be y = KX + B, and substitute m (0,5) and P (2,3) into it
{b=5
 2k+b=3
The solution is: {k = - 1
            b=5
The linear function is y = - x + 5
 
When the point m coordinate is (0, - 5), let the first-order function be y = KX + B, and substitute m (0, - 5) and P (2,3) into it
{b=-5
 2k+b=3
The solution is: {k = 4
            b=-5
The linear function is y = 4x-5

If the image of function y equals MX - {4m-4} passes through the origin, then M = several, what is the function
Can you tell me the process?

If it passes through the origin, it passes (0,0), so m = 1, which is a positive proportional function (also a linear function)