17. with the line x - 3y - 2 = 0.
Find the equation of lines passing through the point (1,-4) and making an angle of 135º

The equation of the line passing through the point (1,-4) and making an angle of 135º will be:

Step-by-step explanation:

Given the point (1, -4)

Given that the line makes an angle of 135º.

so

Slope = m = tan 135º = -1

Using the point-slope form of the line equation

where m is the slope of the line and (x₁, y₁) is the point

substituting the values m = -1 and the point (1,-4)

subtract 4 from both sides

simplify

Therefore, the equation of the line passing through the point (1,-4) and making an angle of 135º will be:

, 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