Point A'(2,3)A ′
(2,3)A, prime, left parenthesis, 2, comma, 3, right parenthesis is the image of A(3,-4)A(3,−4)A, left parenthesis, 3, comma, minus, 4, right parenthesis under a translation.

The slope of the line through the points is -5/7

Step-by-step explanation:

Here, we want to calculate the value of the slope through the lines

Mathematically;

m = y2-y1/(x2-x1)

Where (x1,y1) = (-4,2)

and (x2,y2) = (3,-3)

Substituting these values, we have;

m = (-3-2)/(3-(-4)) = -5/7 = -5/7

, and

for

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote , , , so that we can call

note the following:

the pattern: to get the next term value, we just add the next term number (e.g. 1st, 2nd, to the previous term value (term values are the given numbers in the question, 1, 3, 6, 10, 15,

from , to get to , we add

from , to get to , we add

etc.

we need to form a recursive formula, a formula that has the next term as a function of the previous term. so a possible recursive formula can be

, and for