1. The linear equation is calculated as follows:

1, point inclination: when the straight line passes through the point (x0, y0) and the slope is k, the linear equation is y-y0 = k (x-x0).

2. Oblique formula: the intercept of a given straight line on the Y axis is B, the slope is K, and the straight line equation is Y = KX+B. ..

3. Two-point formula: If a straight line passes through two points (P 1(x 1, y 1) and P2(x2, y2), the straight line equation is x-x1= y-y.

4. Intercept formula: Given that the intercepts of a straight line on the X axis and Y axis are A and B, the linear equation is X/A+Y/B = 1.

5. General formula: Any straight line can be written in the form of AX+BY+C = 0 (A and B are not 0 at the same time).

Second, the general slope of the linear equation is as follows:

1. The general formula of linear equation: Ax+By+C=0(A≠0 B≠0) is applicable to all straight lines.

2. Slope refers to the tangent value of the angle between the straight line and the horizontal axis and the semi-axis direction of the plane rectangular coordinate system, that is, the slope of the straight line relative to the coordinate system. The general formula is: k =-a/b.

3. Cross intercept refers to the distance between the point (a, 0) where a straight line intersects the horizontal axis and the origin. The general formula is: a =-c/a.

4. Vertical intercept refers to the distance between the point (0, b) where the straight line intersects the vertical axis and the origin. The general formula is: b =-c/b.

Third, the general method of solving linear equations:

1, direct method: according to the known conditions, select the appropriate form of linear equation and directly solve the linear equation. Several forms of linear equations and their respective characteristics should be made clear, and the solutions should be chosen reasonably. As we all know, the point oblique type is usually chosen. Given the slope, choose inclined type or point inclined type; It is known that the intercept on two coordinate axes uses the intercept formula; It is known that two points use two-point formula.

2. undetermined coefficient method: firstly, establish a straight line equation, then calculate the assumed coefficient according to the known conditions, and finally substitute it into the straight line equation. The undetermined coefficient method is often suitable for oblique cutting, and the coordinates of two points are known.

3. Steps of solving linear equation by undetermined coefficient method: setting equation; Find the coefficient; Substitute into the equation to get the linear equation. If a straight line is known to pass through a fixed point, the equation can be solved obliquely by using the point of the straight line, or in the form of oblique truncation and truncation.

Fourth, the expression form of linear equation

1, the general formula: Ax+By+C=0(A and B are not 0 at the same time) is applicable to all straight lines.

K=-A/B，b=-C/B

A1/a2 = b1/b2 ≠ c1/c2 ←→ Two straight lines are parallel.

A1/a2 = b1/B2 = c1/C2 ←→ Two straight lines coincide.

Cross intercept a=-C/A

Longitudinal intercept b=-C/B

2. Point skew: y-y0=k(x-x0) is suitable for straight lines that are not perpendicular to the X axis.

Represents a straight line with a slope of k and passing through (x0, y0).

3. Interception formula: x/a+y/b= 1 is applicable to straight lines that are not perpendicular to the origin or the X and Y axes.

Represents a straight line intersecting the X axis and the Y axis, with the X axis intercept a and the Y axis intercept b..

4. Oblique section: y=kx+b is suitable for straight lines that are not perpendicular to the X axis.

Represents a straight line with a slope of k and a y-axis intercept of b.

5. Two-point formula: applicable to straight lines that are not perpendicular to the X and Y axes.

Straight lines representing (x 1, y 1) and (x2, y2).

(y-y 1)/(y2-y 1)=(x-x 1)/(x2-x 1)(x 1≠x2，y 1≠y2)

6. Intersection point: f 1(x, y)*m+f2(x, y)=0 is applicable to any straight line.

A straight line passing through the intersection of the straight line f 1(x, y)=0 and the straight line f2(x, y)=0.

7. Point hierarchy formula: f(x, y)-f(x0, y0)=0 is applicable to any straight line.

A straight line passing through the point (x0, y0) and parallel to the straight line f(x, y)=0.

8. The normal formula: X COS α+YSIN α-P = 0 is suitable for straight lines that are not parallel to the coordinate axis.

A vertical line segment that passes through the origin and becomes a straight line. The inclination of the straight line where the vertical line segment is located is α, and p is the length of the line segment.

9. Point-by-point formula: (x-x0)/u=(y-y0)/v(u≠0, v≠0) is applicable to any straight line.

A straight line passing through point (x0, y0) has a direction vector of (u, v).

10, the normal formula: a(x-x0)+b(y-y0)=0 is applicable to any straight line.

A straight line passing through the point (x0, y0) and perpendicular to the vector (a, b).