Name______

Writing the Equation of a Line

When you find the equation of a line it will be because you are trying to draw scientific information from it. In math, you write equations like y = 5x + 2 This equation is useless to us. You will never graph y vs. x. You will be graphing actual data like velocity vs. time. Your equation should therefore be written as v = (5 m/s2) t + 2 m/s. See the difference? You need to use proper variables and units in order to compare it to theory or make actual conclusions about physical principles. The second equation tells me that when the data collection began (t = 0), the velocity of the object was 2 m/s. It also tells me that the velocity was changing at 5 m/s every second (m/s/s = m/s2). Let’s practice this a little, shall we?

Force vs. mass F (N)

y = 6.4x + 0.3

m (kg)

You’ve just done a lab to see how much force was necessary to get a mass moving along a rough surface. Excel spat out the graph above. You labeled each axis with the variable and units (well done!). You titled the graph starting with the variable on the y-axis (nice job!). Now we turn to the equation. First we replace x and y with the variables we actually graphed:

F = 6.4m + 0.3

Then we add units to our slope and intercept. The slope is found by dividing the rise by the run so the units will be the units from the y-axis divided by the units from the x-axis. The y-intercept will have the same units as the y-axis. This gives us

F = (6.4N/kg) m + 0.3N

Notice that we do not add units to variables because they stand for values that already contain units.

Use the labels on the graphs to convert the following line equations into physics equations.

1. 2.

-1 p (kg m/s) 1/xo(cm )

-1 t (s) 1/xi (cm ) line equation: y = 15x + 5 line equation: y = -1.1x + 0.05 physics equation: ______physics equation: ______

3. 4.

∆V (V) T2 (s2)

I (A) m (kg) line equation: y = 335x - 2 line equation: y = 5x + 0.1 physics equation: ______physics equation: ______

5. Using these techniques, on the next page make a graph of Height vs. Time (y vs. x), draw a best fit straight line, and determine the full equation of the line…

h (meters) t (seconds) 0.00 0.00 0.56 1.00 1.04 2.00 1.48 3.00 2.13 4.00 2.59 5.00 2.94 6.00 3.77 7.00 4.51 8.00

Show any relevant work and calculations in the space below.