Specifically, for a given straight line, its equation can be expressed as y=ax+b, where a and b are constants. The slope k is a, that is, the slope k=a of this straight line. In addition, if there are two points on a given straight line L, A=(x 1, y 1) and B=(x2, y2), then the slope of the straight line K =(y2-y 1)/(x2-x 1).
The definition of slope m is the tangent of the inclination angle of the straight line, that is, the tangent of the included angle between the straight line and the positive direction of the X axis. The greater the slope, the steeper the straight line; The smaller the slope, the flatter the straight line. When the slope is 0, the straight line is parallel to the X axis, that is, the straight line is horizontal; When the slope does not exist, the straight line is perpendicular to the X axis, that is, the straight line is vertical.
The slope of a straight line is very important for understanding the properties and geometric significance of a straight line. First of all, the slope can be used to judge the increase or decrease of a straight line. When the slope m>0 indicates that Y increases with the increase of X, that is, the straight line is increasing function; When the slope m
The slope is also related to the length and angle of the straight line.
If we know the length and slope of the straight line, we can find the intercept of the straight line; If we know the intercept and slope of a straight line, we can find the length of the straight line. At the same time, the angle between the straight line and the coordinate axis can be calculated by using the slope.
The slope of a straight line is not only widely used in geometry, but also of great significance in many fields such as physics, engineering and economy. For example, in physics, slope can be used to describe the motion law of objects; In engineering, slope can be used to analyze the law of mechanical motion; In economics, slope can be used to analyze the relationship between money supply and price level.