4.1 Writing Equations - y=mx+b definition

The slope, denoted by the letter "m," is a measure of the steepness or slant of a line. It represents the ratio of the vertical change (rise) to the horizontal change (run) between any two points on the line. In other words, it is the change in y (vertical change) divided by the change in x (horizontal change). The slope is defined as follows:

m = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are any two points on the line. If the slope is positive, the line is increasing from left to right; if the slope is negative, the line is decreasing from left to right; and if the slope is zero, the line is horizontal. The slope is an important concept in algebra and geometry and is used to describe and analyze linear relationships between variables.

The y-intercept, denoted by the letter "b," is the point where a line crosses or intersects the y-axis. It is the value of y when x is equal to zero. In other words, it is the point on the line where x=0. The y-intercept is an important part of the equation of a line in slope-intercept form, which is y = mx + b, where "m" is the slope of the line and "b" is the y-intercept. The y-intercept tells us where the line intersects the y-axis and gives us a starting point to graph the line. For example, if the equation of a line is y = 2x + 3, the y-intercept is 3, which means that the line crosses the y-axis at the point (0, 3).