Answer:2. Rate of change, or slope, is the change in y over change in x. Remember that a point is given in (x, y). Also that you need two points to find the change.
If you have two points, (x1, y1) and (x2, y2), the rate of change or slope
In your problem, the given points are (0, -1) and (2, -11)
The "initial value" is the y-intercept - where the graph intersects the y-axis and also where x = 0. The given point (0, -1) has x = 0, so the initial value is -1.
4. Remember the model equation for a graph of a line is
y = mx + b,
where m is slope and b is y-intercept - where the graph intersects the y-axis and also where x = 0.
The x-axis of the graph would be number of weeks, since it is independent.
The y-axis of the graph would be how much money she has.
Since she starts (at 0 weeks) at $25, the first point would be (0, 25). Notice here that it is the y-intercept since x = 0. The value of b in the model equation of a line y = mx + b would be 25.
The rate of change, or slope, is $5/week. This is m in the model equation of a line y = mx + b.
Putting b = 25 and m = 5 into the model equation y = mx + b (remember we use this equation because it works for all lines), the equation would be
y = 5x + 25.
4.
The slope of this will be -0.5degrees/hr, or just -0.5 if it is used as m in the
y = mx+b equation. The slope is negative because it "decreases".
5.
Plot each point and connect the dots. Remember the first number corresponds to the x-axis and the second to the y-axis.
For example in the table for x = -2 and y = -6, the point is (-2, -6), and from the origin (0,0) you go left 2 on the x-axis and down 6 to plot the point.
9.
I think you can do this if you can do #3, but now you have to find b by plugging in given values.
y = mx + b
y = 1212x + b
We can plug in the given point (3,1) to find b.
1 = 1212(3) + b
b = -3625
y = 1212 - 3625
10. Don't know which function you are referring to.
The slope is $10/week, or m = 10.
A point is (4, 90) because "After 4 weeks, Roberta has $90."
The y-intercept is 50 because x (weeks) = 0 at that time.
y = mx + b
y = 10x + 50
, we have for 
the Taylor series expansion about 0 as
with 
, so that the series is equivalent to
, we have
