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Slope definition:

Slope, also known as "angle coefficient", indicates the inclination of a straight line relative to the abscissa axis in a plane rectangular coordinate system.

The tangent value tanα of the inclination angle α of a straight line with respect to the X axis is called the "slope" of the straight line, denoted as k, and the formula is k=tanα. It is stipulated that the slope of the straight line parallel to the X axis is zero, and the slope of the straight line parallel to the Y axis does not exist. For a straight line passing through two known points (x 1, y 1) and (x2, y2), if x 1≠x2, the slope of the straight line is k = (y1-y2)/(x/kloc-0).

Coverage:

Curriculum standard: In the compulsory education stage, students learn a 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. Any fraction y/x 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 the slope i=tanθ=y/x and the 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.

Mathematics: First of all, from a practical point of view, the slope is the slope, which is the average change rate of height. Slope is used to describe the inclination of the road, that is, the ratio of the tangent height of the slope to the horizontal length, which is equivalent to moving one kilometer in the horizontal direction and rising or falling in the tangent direction. This ratio actually indicates the size of the slope.

Secondly, the tangent value from the inclination angle; There is also the angle between the vector in the upward direction of the straight line and the unit vector in the X axis direction. Finally, the concept of slope is re-recognized from the perspective of derivative. Slope is actually the instantaneous rate of change of vertical axis with horizontal axis.

Understanding the concept of slope not only plays an important role in future study, but also helps to learn some important mathematical problem solving methods in the future.

Textbook: From the outline, when dealing with the knowledge of the slope of a straight line, the textbook first talks about the inclination of the straight line, then the slope of the straight line, and then introduces the derivation of the slope formula of two points on the straight line.

Judging from the new curriculum standard, we can see that the textbook A of People's Education Edition first talks about the inclination of a straight line, and then about the slope of a straight line, only in the form of questions.

Physics: Physics class in senior high school needs to analyze, solve and calculate physical phenomena and processes by using images of average speed, instantaneous speed, acceleration and other physical quantities and time (or other physical quantities).

Quantitative research on laws and trends through images and coordinates is also widely used in science, engineering and business in universities.

Derive and understand formulas: Slope can help people to better deduce and understand formulas and so on.