1. Objective The student will be able to: find the slope of a line given 2 points and a graph.

2. What is the meaning of this sign? 1.Icy Road Ahead 2.Steep Road Ahead 3.Curvy Road Ahead 4.Trucks Entering Highway Ahead

3. What does the 7% mean? 7% IS THE SLOPE OF THE ROAD. IT MEANS THE ROAD DROPS 7 FEET VERTICALLY FOR EVERY 100 FEET HORIZONTALLY. 7% So, what is slope??? Slope is the steepness of a line. 7 feet 100 feet

4. Slope can be expressed different ways: A line has a positive slope if it is going uphill from left to right. A line has a negative slope if it is going downhill from left to right.

5. When given the graph, it is easier to apply “rise over run”. 1) Determine the slope of the line.

6. Start with the lower point and count how much you rise and run to get to the other point! Determine the slope of the line. 6 3 run 3 6 == rise Notice the slope is positive AND the line increases!

7. 2) Find the slope of the line that passes through the points (-2, -2) and (4, 1). When given points, it is easier to use the formula! y 2 is the y coordinate of the 2 nd ordered pair (y 2 = 1) y 1 is the y coordinate of the 1 st ordered pair (y 1 = -2)

8. Did you notice that Example #1 and Example #2 were the same problem written differently? (-2, -2) and (4, 1) 6 3 You can do the problems either way! Which one do you think is easiest?

9. Find the slope of the line that passes through (3, 5) and (-1, 4). 1.4 2.-4 3.¼ 4.- ¼

10. 3) Find the slope of the line that goes through the points (-5, 3) and (2, 1).

11. Determine the slope of the line shown. 1.-2 2.-½ 3.½ 4.2

12. Determine the slope of the line. The line is decreasing (slope is negative). 2 Find points on the graph. Use two of them and apply rise over run.

13. What is the slope of a horizontal line? The line doesn’t rise! All horizontal lines have a slope of 0.

14. What is the slope of a vertical line? The line doesn’t run! All vertical lines have an undefined slope.

15. Determining the equation of the line In Physics we will be using primarily one form of the equation that represents a linear line. y= mx +b y = variable graphed on the y axis (NOT a number unless you are solving for the other variable x) m = slope of the line (rate of change) x= variable graphed on the x axis (NOT a number unless you are solving for the other variable y). b= y-intercept, where the line hits the y axis.

16. Create the equation for the following graphs.

17. Distance Time Graphs UNDERSTANDING AND INTERPRETING DISTANCE- TIME GRAPHS

18. Distance Time Graphs Describing a journey made by an object is not exciting if you just use words. As with much of science, graphs are more revealing. Plotting distance against time can tell you a lot about a journey. Let's look at the axes: Time always runs horizontally (the x-axis). The arrow shows the direction of time. The further to the right, the longer time from the start. Distance runs vertically (the y-axis). The higher up the graph we go, the further we are from the start.

19. Not moving? This is what it looks like… If something is not moving, a horizontal line is drawn on a distance-time graph (dt-graph). Time is increasing to the right, but its distance does not change. It is stationary.

20. Moving…. If something is moving at a steady speed, it means we expect the same increase in distance in a given time: Time is increasing to the right, and distance is increasing steadily with time. It moves at a steady speed.

21. Steady Speed… If something is moving at a steady speed, it means we expect the same increase in distance in a given time: Time is increasing to the right, and distance is increasing steadily with time. It moves at a steady speed. On a distance vs. time graph, speed = the slope of the line.

22. Can you describe what is going on here? For the first part of the journey shown by the graph below, the object moved at a steady (slow) speed. It then suddenly increased its speed, covering a much larger distance in the same time. This sort of motion is not very realistic, but is easy to understand. It also makes calculations easier!

23. What is the effect of line ‘Steepness’, A.K.A slope… Both the lines below show that each object moved the same distance, but the steeper yellow line got there before the other one: A steeper gradient indicates a larger distance moved in a given time. In other words, higher speed. Both lines are of constant gradient, so both speeds are constant.

24. There are three parts to the journey shown below: Moving at a steady speed, slowly Not moving for quite some time Moving again, but at higher speed In all the graphs so far, we have not seen any numbers - it's about time we did!

25. Finding speed from these types of graphs! We can see that the motion shown by the yellow line is fastest. By definition, speed = distance / time so the steepness (or gradient) of the line will give us the speed! Yellow: speed = distance / time = 30 m / 10 s = 3 m/s Blue: speed = distance / time = 20 m / 20 s = 1 m/s

26. Calculate the speeds of different sections within a graph Stage 1: speed = distance / time = 100 m / 10 s = 10 m/s Stage 2: speed = distance / time = 50 m / 10 s = 5 m/s Stage 3: speed = distance / time = 150 m / 20 s = 7·5 m/s

27. Equation of the line: Distance-time

28. Slope of d v t Rise = distance Run = time Slope = distance/time -----------  SPEED! Speed = slope of a distance/time graph!