I need to write the equation of the line in slope intercept form

y = 2x + 5

Step-by-step explanation:

Step 1: Find slope

m = (3-1)/(-1+2) = 2

Step 2: Find y-intercept

(0, 5)

Step 3: Write in slope-intercept form

y = mx + b

y = 2x + 5

And we have your answer!

(a) The ONLY explicit rule for the nth term of the sequence is .

Step-by-step explanation:

Here, the given sequence is 7, -7, 7, -7, ...

The first term = 7, Second term = -7, Third term =-7 and so on..

Now check the given sequence for each given formula, we get:

(1)  

Now, for n = 1 :

Similarly, for, n = 2:  

Hence, the given formula satisfies the given sequence.

(2)  

Now, for n = 1 :

But, First term = 7

Hence, the given formula DO NOT satisfy the given sequence.

(3)  

Now, for n = 1 :

Similarly, for, n = 2:  

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

(4)

Now, for n = 1 :

Similarly, for, n = 2:  

But, Second term = -7

Hence, the given formula DO NOT satisfy the given sequence.

So, the ONLY explicit rule for the nth term of the sequence is .