SOLUTION: Can someone please help me with these two problems: 1.Find an equation of the line satisfying the given condidtions Through(0,2); m=3/2 2. Find the indicated term of the geo

Question 201863: Can someone please help me with these two problems:
1.Find an equation of the line satisfying the given condidtions
Through(0,2); m=3/2
2. Find the indicated term of the geometric sequence
a=-3, r=-4; find the 7th term
a. 3072
b. 196,608
c. -4096
d. -12,288
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

If you want to find the equation of line with a given a slope of which goes through the point (,), you can simply use the point-slope formula to find the equation:

---Point-Slope Formula---
where is the slope, and

is the given point

So lets use the Point-Slope Formula to find the equation of the line

Plug in , , and (these values are given)

Distribute

Multiply and to get

Add 2 to both sides to isolate y

Combine like terms and to get
------------------------------------------------------------------------------------------------------------
Answer:

So the equation of the line with a slope of which goes through the point (,) is:

which is now in form where the slope is and the y-intercept is

Notice if we graph the equation and plot the point (,), we get (note: if you need help with graphing, check out this solver )

Graph of through the point (,)
and we can see that the point lies on the line. Since we know the equation has a slope of and goes through the point (,), this verifies our answer.

# 2

The general form of ANY geometric sequence is where "n" starts at 1 (the formula is slightly different if you start at different "n" values)

Start with the given equation.

Plug in and (these values are given)

Plug in (for the 7th term)

Subtract

Raise -4 to the 6th power to get 4,096

Multiply

So the 7th term is -12,288 which means that the answer is D)
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