Find the slope of the line parallel to each given line
y=2/3x-2
y=9/5-5
write the slope intercept form of each equation
x-2y=7
7x+2y=-28
2x+3y=-6
2x+3y=-7

When the equation of a line is written in the form of

                 Y = (first number) x + (second number)

then the first number is the slope of the line, and the second number
is the "y-intercept" ... the height where the line crosses the y-axis.
This form of the equation is called the "slope - intercept" form, because
when the equation is in that form, the slope and intercept are so obvious.

Both of the first two examples are written in that form, so you can read
the slope directly from the equations. 
The slope of the first one is  2/3 .

Now, here's a Very Important Factoid:  Parallel lines have the same slope.

So a line parallel to the first example has a slope of  2/3 .

Now I'm sure you can do the second one on your own.



The second set of examples just wants you to write each one in that form.
That just means to solve each equation for 'y'. 

When you do that, you'll have  Y = (first number) x + (second number)
and that's the "slope-intercept" form.

First one:                            x - 2y = 7

Subtract 'x' from each side:    -2y = -x - 7
Divide each side by  2 :           -y = -1/2 x - 7/2
Multiply each side by -1 :          y = 1/2 x + 7/2

Second one:                   7x + 2y = 28

Subtract 7x from each side:    2y = -7x + 28
Divide each side by  2 :            y = -7/2 x + 14

Now I think you can do the other two on your own.

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step-by-step explanation:

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

1 the 1st term, 3 the 2nd term, 6 the 3rd term,etc.

note the following:

from the 1st term (1) to the 2nd term (3), we go up by 2,from the 2nd term (3) to the 3rd term (6), we go up by 3from the 3rd term (6) to the 4th term (10), we go up by 4, andfrom the 4th term (10) to the 5th term (15), we go up by 5.

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