what is the meaning of the slope

Question

The equation for the speed (not the height) of a ball that is thrown up straight in the air is given by v=128-32t, where v is the velocity in feet per second and t is the number of seconds after the ball is thrown. With what initial velocity was the ball thrown? What is the meaning of the slope?

 

 

Hiya! I have no idea where to begin with this problem. Please help me solve this. Thanks much

Answer 1

The initial velocity is the velocity at time 0.  In this case v(0) = 128 - 32(0) = 128 ft/s.  The slope in this scenario is -32, which means that the velocity decreases by 32 ft/s for every second that passes.  Remember, slope is the change in y over the change in x.  If you were to rewrite this function in slope-intercept form, it makes it a bit easier to see how the slope affects the scenario described here:

 

y = mx + b

v = -32t + 128