15. tell whether the lines for each pair of equations are parallel perpendicular or neither
y=-3x+7
-2x+6y=3
16. tell whether the lines for each pair of equations are parallel perpendicular or neither
y=-1/5x+6
-2x+10y= 5

Step-by-step explanation:

15. The given lines are

Y=-3x+7 & -2x+6y=3 or, 6y = 3 + 2x or, .

The slope of the first line is -3 and the slope of the second line is [Comparing with the standard form of equation of straight line y = mx + c, where m is the slope of the straight line].

Two straight lines will said to be perpendicular to each other, if the product of its slopes will be equal to -1.

Since, , the equations are perpendicular with respect to each other.

16. The lines are and -2x + 10y = 5 or, 10y = 5 + 2x or, .

As per the question number 15, it is clear that these equations are not perpendicular.

Here, the slope of the first one is and the slope of the second one is .

The values are same with different sign. Hence, these equations are not parallel too.

, 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

slope intercept form is y = mx + b