Finding the expression of linear function is a common problem in linear function. The common questions of such questions are summarized as follows for students' reference.

First, define the type.

Example 1 It is known that the function y=(m-2)xm2-3+5 is a linear function. Find its expression.

The solution is defined by a linear function, knowing that m-2≠0, m2-3= 1, so m=-2.

So the expression of this linear function is y=-4x+5.

There are two points to be paid attention to when defining an expression with a linear function: first, the coefficient of the independent variable is not 0; Second, the number of independent variables is 1, which must be met at the same time. Therefore, this problem should ensure the number of times m2-3= 1 and the coefficient m-2≠0.

Second, alternative type.

Example 2 Given the image intersection point (-2, 1) of the linear function y=kx-3, find the expression of this function.

Solution Because the image of the linear function y=kx-3 passes through (-2, 1), 1=-2k-3, and the solution is k=-2.

So the expression of this linear function is y=-2x-3.

This problem is based on the nature of function: if the function passes through a point, the coordinates of the point satisfy this function relationship, which is also the key to solve this kind of problem.

Example 3 If it is known that the image passing point of a linear function is (2, 1) and the coordinate of the intersection with the Y axis is (0,3), then the expression of this function is.

The expression of solving this linear function is y=kx+b, according to the meaning of the question, 2k+b= 1, b=3, and the solution is k=- 1, b=3.

So the expression of this linear function is y=-x+3, so fill in y=-x+3.

Explain that this is a typical problem of finding the expression by undetermined coefficient method. This method is the most effective and widely used. Students should try their best to understand its essence.

Thirdly, the type of translation.

Example 4 The expression of straight line y=3x- 1 is shifted upward by 3 unit lengths.

Let the expression after translation be y=kx+b, because the two straight lines are parallel before and after translation, so k=3, and the distance from the intersection of the straight line y=kx+b and the Y axis to the origin is 3- 1=2, so b=2, so the expression after translation is y=3x+2, so fill in y=3x+2.

Commentary can also solve this kind of translation problem by combining numbers with shapes, roughly drawing an image and translating according to the meaning of the problem.

Fourth, the regional type.

Example 5 It is known that the triangle area enclosed by the straight line y=kx+6 and the two coordinate axes is equal to 12. Find the expression of this function.

The solution is easy to find that the intersection of a straight line with the X axis is (-6k,0) and the intersection with the Y axis is (0,6), so there is 12? 6k？ 6= 12, and the solution is |k|=32, that is, k = 32. So the expression of this straight line is y=32x+6 or y=-32x+6.

It must be noted in the commentary that there are two kinds of straight lines that meet the conditions in this kind of problems: straight rising time (that is, k>0) and falling time (K