What is an equation of the line that passing through the points (-2, -5) and (4, 7) ?

Step-by-step explanation:

Use the slope-intercept formula: where m is slope and b the y-intercept.

Use the slope formula for when you have two points:

Rise over run is the change in the y-axis over the change in the x-axis. Insert values:

Simplify parentheses (negative+negative=positive)

Simplify

2 is the slope:

Now use one of the points to find the y-intercept by substituting the x and y values into the equation. Solve for b:

(4,7)

The y-intercept is -1. Insert into the equation. Change the + symbol to -:

Done.

, 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