Final answer:
The slope of a line is the measure of its steepness, calculated as the rise over run and depicted by the variable 'm'. An example of a slope of 3 indicates that for every one unit increase in the x-value (run), the y-value (rise) increases by three units. The y-intercept 'b' is where the line crosses the y-axis.
Step-by-step explanation:
The slope of a line, typically represented by the variable m, is a measure that indicates how steep the line is on a graph. It is calculated as the ratio of the rise (change in y-value) to the run (change in x-value). To visualize this, consider a line graph where the horizontal axis represents the x-values and the vertical axis represents the y-values. If you have two points on the line, the slope m is found by dividing the difference in their y-values by the difference in their x-values, which can be expressed as m = Δy/Δx.An easy example to understand this concept is to look at a line on a graph with points plotted at coordinates. If, for each horizontal step to the right (run), the line moves up three units (rise), the slope of the line would be 3. The y-intercept, denoted as b, is another important feature of the line. It shows where the line crosses the y-axis, providing a starting point for the line on the graph. In this example, the line would intersect the y-axis at b = 9 indicating the initial value of y when x is 0.The understanding of slope is crucial not just in algebra, but also in various real-world contexts where interpreting the rate of change is essential, such as in physics for calculating velocity or in economics to understand cost functions.