Question

1. Write the equation of the line through the points (1, -2) and (4, 1)
2. Write the equation of the arithmetic sequence that starts with -7 and each term decreases by 3
a) y = 1/2x +1
b) y - 3 = 1/2 (x -4)
c) x - 2y = -2
d) f(0) = 1, f(n) = f(n - 1) + 1/2
1. Verify that the four equations above are equivalent.
2. Explain how you know that the four equations are linear.
3. You have been appointed as a mathematics efficiency expert. Your job is to compare these four forms of equations for different uses and decide which form is most efficient and effective for each use. CONTINUED ↓ ↓

Answer 1

The investigation will be conducted in four parts with a report to be written at the end.

4. What is the important difference between the type of situations that can be modeled with a recursion formula and the other equation forms?

Answer 2

Sorry I just moved to a new school in the middle of the semester, so I don't understand any of this :(

Answer 3

for the first one:
first find the slope.
y2-y1/x2-x1 = 1-(-2)/ 4-1= 4/3
then you must plug in the points and the slope into y-y1=m(x-x1)
y-1=3/4(x-(-2))
y-1=3/4x- 6/4
y-1=3/4x-3/2
add 1 on both sides
y=3/4x-3/2+1
since you cannot add fractions that don't have a common denominator, you must multiply the top and the bottom by 2
3/2 + 2/2 = 5/2
so therefore the equation is:
y=3/4x+ 5/2
I believe that is right.

Answer 4

Thank you sooo much @pinkanchor212

Answer 5

no problem!