Mathematics, 16.12.2019 10:31, haleyehewitt2001

Consider the line y = -8x+
find the equation of the line that is perpendicular to this line and passes through the point (-4, 4).
find the equation of the line that is parallel to this line and passes through the point (-4, 4).
equation of perpendicular line:
equation of parallel line:

Answers: 2

Show answers

Answers

answered: hidagiser

Part 1) The equation of the perpendicular line is $y=\frac{1}{8}x+\frac{9}{2}$

Part 2) The equation of the parallel line is y=-8x-28

Step-by-step explanation:

Part 1) Find the equation of the line that is perpendicular to the given line and passes through the point (-4, 4)

The slope of the given line is m=-8

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal (the product of the slopes is equal to -1)

The slope of the line perpendicular to the given line is

$m=\frac{1}{8}$

Find the equation of the perpendicular line in point slope form

y-y1=m(x-x1)

we have

$m=\frac{1}{8}$

$point\ (-4,4)$

substitute

$y-4=\frac{1}{8}(x+4)$

Convert to slope intercept form

y=mx+b

isolate the variable y

apply distributive property right side

$y-4=\frac{1}{8}x+\frac{1}{2}$

$y=\frac{1}{8}x+\frac{1}{2}+4$

$y=\frac{1}{8}x+\frac{9}{2}$

Part 2) Find the equation of the line that is parallel to the given line and passes through the point (-4, 4)

The slope of the given line is m=-8

Remember that

If two lines are parallel, then their slopes are the same

The slope of the line parallel to the given line is

m=-8

Find the equation of the parallel line in point slope form

y-y1=m(x-x1)

we have

m=-8

$point\ (-4,4)$

substitute

y-4=-8(x+4)

Convert to slope intercept form

y=mx+b

isolate the variable y

apply distributive property right side

y-4=-8x-32

y=-8x-32+4

y=-8x-28

answered: Guest

It says in the questions that it is 6.5?

answered: Guest

$a_1 = 1$ , and

$a_{n+1} = a_n + (n + 1)$ for $n \ge 1$

step-by-step explanation:

we can analyze the pattern at which the terms increase. let us denote $a_1 = 1$ , $a_2 = 3$ , $a_3 = 6$ , 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 $a_1 = 1$ , to get to $a_2 = 3$ , we add $2(=1+1)$