Slope introduction:
Mathematical terms are quantities that indicate the inclination of a straight line (or tangent of a curve) with respect to a (horizontal) coordinate axis. It is usually expressed by the tangent of the angle between a straight line (or the tangent of a curve) and a (horizontal) coordinate axis, or the ratio of the difference between the ordinate and abscissa of two points.
Slope, also known as "angle coefficient", is the tangent of the positive included angle of a straight line relative to the horizontal axis, reflecting the inclination of the straight line relative to the horizontal plane. The tangent value of the angle formed by a straight line and the positive and semi-axis directions of the horizontal coordinate axis of the plane rectangular coordinate system is the slope of the straight line relative to the coordinate system.
If the straight line is perpendicular to the X axis, then the tangent of the right angle is tan90, so the straight line has no slope (it can also be said that the slope of the straight line is infinite). When the slope of the straight line L exists, for the linear function y=kx+b (oblique section), k is the slope of the function image.
In the compulsory education stage, students learn the function once, and its geometric meaning is represented by a straight line. The coefficient of the first term is the slope of the straight line, but it cannot be expressed when the straight line is perpendicular to the X axis. Although the term slope is not clearly given, in fact, the idea has penetrated into it.
In senior high school, compulsory one and compulsory two discussed the problem of straight line, and elective one and elective two also mentioned some problems related to straight line. The contents listed above actually involve the concept of slope, so it can be said that the concept of slope is one of the important mathematical concepts that students gradually accumulate.
Slope is an important knowledge point in middle school mathematics. For any fraction y/x, it can be regarded as the slope of the connecting line between point P(x, y) and origin o (0,0), and it also involves the undetermined coefficient k in slope i=tanθ=y/x and linear function y=kx+b;
The knowledge of straight line, arithmetic progression and derivative in senior high school mathematics is more closely related to slope. Slope is not only an algebraic problem, but also its geometric significance, which embodies the mathematical idea of combining numbers with shapes.