The slope knowledge points of high school mathematics straight line are summarized as follows:

1. Slope of straight line

When the slope of the straight line L exists, the formula of oblique section y=kx+b is k=0 and y = b.

When the slope of the straight line L exists, the point inclination angle Y2-Y 1 = K (X2-X 1),

When the straight line L has a non-zero intercept on two coordinate axes, there is an intercept formula X/a+y/b= 1.

For any point on any function, its slope is equal to the included angle between its tangent and the positive direction of X axis, that is, tanα.

Slope calculation: ax+by+c=0, where k =-a/b.

Linear slope formula: k=(y2-y 1)/(x2-x 1)

The product of slopes of two vertically intersecting lines is-1:k1* k2 =-1.

When k>0, the greater the angle between the straight line and the X axis, the greater the slope; When k < 0, the greater the angle between the straight line and the X axis, the smaller the slope.

2. Inclination and slope

1) The concept of straight line inclination: when the straight line L intersects with the X axis, the angle α formed by the positive direction of the X axis and the upward direction of the straight line L is called the inclination of the straight line L, especially when the straight line L is parallel or coincident with the X axis, α = 0.

2) The value range of inclination angle α: 0 ≤ α.

3. Slope of the straight line:

The tangent of the inclination angle α (α ≠ 90) of a straight line is called the slope of this straight line, and the slope is often expressed by lowercase letter K, that is, k=tanα.

(1) When the straight line L is parallel or coincident with the X axis, α = 0 and k = tan0 = 0.

⑵ When the straight line L is perpendicular to the X axis, α = 90, and k does not exist.

Therefore, the inclination angle α of the straight line L must exist, but the slope k does not.

4. Straight line slope formula:

Given two points p 1 (x 1, y 1), p2 (x2, y2), x 1 ≠ x2, the slope of the straight line P 1P2 is expressed by the coordinates of two points:

Slope formula: k=y2-y 1/x2-x 1.

5. Parallelism and verticality of two straight lines

1) Both straight lines have slopes and do not overlap. If they are parallel, their slopes are equal; On the contrary, if their slopes are equal, they are parallel, that is,

Note: The above equivalence is established on the premise that two straight lines do not coincide and the slope exists. Without this premise, the conclusion will not be established. That is to say, if k 1=k2, then there must be l 1∑L2.

2) Both straight lines have slopes. If they are perpendicular to each other, their slopes are negative reciprocal. On the contrary, if their slopes are negative reciprocal, they are perpendicular to each other.