Miguel wrote two equations. he thinks the two equations represent parallel lines. is he correct? explain why or why not.
-2x+6y=-42
y+10=1/3(x-3)

Yes, he is correct because both the lines have same slope.

Step-by-step explanation:

Given:

The two equations are:

Two lines are parallel only if their slopes are equal.

So, let us write each equation in slope-intercept form , where, is the slope of the line.

Equation 1 is:

So, the slope of line 1 is

Now, equation 2 is:

Therefore, slope of line 2 is,

∵

Therefore, both the lines are parallel to each other.

idk

step-by-step explanation:

maybe try   if it is work from a book, if not try

, 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