class 051014
These questions are from your homework on the worksheet entitled 'The Slope = Slope Equation'. Using the homework you have done, quickly give answers to these questions:
1. If we know that (3, -4) is a data point on a line with slope 2.8, what is the equation of the line?
Using y = m x + b, we know that the slope is 2.8 so we have
y = 2.8 x + b.
We also know that (3, -4) is a data point so
-4 = 2.8 * 3 + b.
Solving for b we get
b = -4 - 2.8 * 3 = -12.4.
2. Find the linear function depth(t) = mt + b if it is known that at clock time 30 seconds the depth is 50 centimeters, and that depth is changing at a rate of -.35 centimeters/second.
We know that depth(30) = 50 cm and that the rate of depth change is -.35 cm/sec. So we know depth(30), and we know m.
Since m = -.35 cm/s,
depth(t) = -.35 cm/s * t + b.
Since depth(30) = 50 cm we have
50 cm = -.35 cm/s * 30 sec + b so that
b = 50 cm -.35 cm/s * 30 sec = 50 cm - 10.5 cm = 39.5 cm.
5. Suppose a line passes through (3, -2) with slope 5. What is the slope = slope equation (y - y1) / (x - x1) = m when we substitute these values? What do we get when we solve for y?
The slope is (y - y1) / (x - x1) = (y - (-2) ) / ( x - 3) = (y + 2) / (x - 3).
The slope is 5.
So
(y + 2) / ( x - 3) = 5.
Solving for y we multiply both sides by (x - 3) to get
(y + 2) = 5 ( x - 3) so that
y + 2 = 5 x - 15 and
y = 5x - 15 - 2 or
y = 5x - 17.
Substitute the above values x = 3, y = -2 and m = 5 into the form y = mx + b. Solve for b. Then substitute m and b into the form y = mx + b to obtain the equation of the line.
Substituting we get
-2 = 5 * 3 + b so that
b = -2 - 5 * 3 = -17.
Thus our equation is
y = 5 x - 17.
Compare the equations you obtained from the different methods.
Make a statement about whether or not the two methods seem to give the same results.
8. Assume that the average class grade in this course is a linear function of how many hours of intelligent out-of-class effort students put into it, on the average. Suppose that an average of 40 hours of such effort was sufficient to make an average grade, on a 4-point scale, of 1.2, and that each additional hour added .045 points to this average. Find the linear function pointAverage(aveHours) that models this situation.