Wednesday, September 18, 2013

TO FIND THE Y-INTERCEPT AND SLOPE FROM THE GRAPH


Y-intercept:



The y-intercept must be read off the graph, on the appropriate axis, not figured out using calculations. 

If the y-intercept does not appear on the graph, change your scale and regraph until the problem is fixed. 

Be careful when you read it that you are looking at the y-axis, i.e. that is that you are looking at the line through x = 0, sometimes it lies in the middle of your piece of paper rather than on the left hand side.


Slope:



To find the slope, use "rise vs run", (y2-y1)/(x2-x1), with "point 1" and "point 2" being points on the best fit line – just make sure those don't happen to be data points, that is that they don't correspond to values that you measured in the lab, or put another way, values that you have on your table.
So the order in which you need to do things is:
- indicate the data points (functions of what you measured) on the graph paper. Then forget about your table, you should never look at it again!
- draw a best fit line, that is straight line that fits those points, NOT a "connect the dots" zigzag thing. And only use those points, don't take the origin into account.
- Once you have the best fit line, imagine that is all you've got, don't even look at the points you used to find it. Calculate the slope in the same way as you would if you were just given that one line and the axes, and told "There, here's a straight line. Find its slope".  That is, choose two points on that best fit line (again, just make sure those don't happen to be data points, point you put on yourself).  Find the coordinates of these two points by reading these coordinates on the axes, and then use these coordinates to find the slope by calculating "rise over run".