Slope is a fundamental concept in mathematics that measures how steep a line is and in which direction it goes. When we look at a line on a coordinate plane, the slope tells us how much the line rises or falls as we move from left to right. It's the ratio of vertical change to horizontal change between any two points on the line.
The slope formula gives us a precise way to calculate the steepness of a line. It's written as m equals y2 minus y1 divided by x2 minus x1, where m represents the slope, and the two points are any distinct points on the line. In our example, using points (1, 1.5) and (3, 2.5), we calculate: y2 minus y1 equals 2.5 minus 1.5 which is 1, and x2 minus x1 equals 3 minus 1 which is 2. Therefore, the slope is 1 divided by 2, which equals 0.5.