Learn about Slope Line Applications In this lesson let’s learn about how we apply the slope a line to real life examples. So let’s say Mark is driving from New York to New Jersey at 3 pm he has hired an 80 miles from New York, at 5:30 pm he is 330 miles from New York graft the line the represents marks Distance from New York at any given time. And we need to find and I need to put the slope of the line so here’s what we know at 3 pm he is 180 miles from where he started at 5:30 pm he is 330 miles from he started. Now here’s what we going to do we going to apply what we know about the slope of a line to solve this so what we going to do is drag rough on one axis is time, on the other axis is distance. So as we can see if we draw a line the slope of a line tells you the rate of change. The slope of a line tells you rate of change. How fast are things changing? So in this case what is changing, well time changes and distance from New York changes. So if we plot the two points that we have which is at 3pm which is 3 hours he is 180 miles so I apply at 3 and 180, point 1 and then at 5:30 which is 5 ½ he is 330 miles and I draw a line between this, this is the average speed at which Mark is going. Was it y is the average speed because 1axis is distance and the other axis is time. So distance over time is speed. So what’s Mark’s average speed? Mark’s average speed equals the slope that we are calculating. So let’s calculate the slope the we’re given the coordinates right here it’s 3 hours an 180 miles so that’s your coordinate 5 ½ hours in 3:30. So let’s do y2 – y1 over x2 – x1. What is the second y coordinate that’s here? 330. First, y coordinate 180 over difference in the x coordinates 5.5 – 3. What am I left with? 330 – 80 is 150 over 5 ½ - 3 is 2.5. This means this is 60. So the slope of the line is 60and since the slope is distance over time marks average speed is 60 in miles per hour because this in miles and this is in hours so his average speed on this drive is 60 miles an hour we could do that by simply plotting the graph and using the slope formula.