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On average, the price of gas increased by about 19.6¢ each year. Other examples of rates of change include: A population of rats increasing by 40 rats per week. A car traveling 68 miles per hour (distance traveled changes by 68 miles each hour as time passes)
The concept of slope is important in economics because it is used to measure the rate at which changes are taking place. Slope shows both steepness and direction. With positive slope the line moves upward when going from left to right. With negative slope the line moves down when going from left to right.
Have students work on understanding the connection between the concept and the real-world meaning, such as a y-intercept indicating a one-time charge or base fee for something, while the slope indicates the rate for a service based on time or some other unit.
The slope is defined as the ratio of the vertical change between two points, the rise, to the horizontal change between the same two points, the run. The slope of a line is usually represented by the letter m. (x1, y1) represents the first point whereas (x2, y2) represents the second point.
Slope describes the steepness of a line. The slope of any line remains constant along the line. The slope can also tell you information about the direction of the line on the coordinate plane. Slope can be calculated either by looking at the graph of a line or by using the coordinates of any two points on a line.
The gradient of the area function(As in the area bounded by this graph and the x axis) is the height of this line. So if the line is y=4 then the area under this grows at a rate of 4 per x. It is the same idea for any function. The height of that function represents the gradient of the area function.
The hypotenuse of the triangle (the diagonal) is the line you are interested in finding the slope of. The two ‘legs’ of the triangle are the ‘rise’ and ‘run’ used in the slope formula. Slope = rise/run.
The slope gradient is the angle of incline or decline, expressed in the percent of rise or fall of the soil surface from horizontal over a distance of 100 feet. Soil slope affects the flow of water that can erode the soil.
rise over run