Consider the graph of the line y = x – 4 and the point (−4, 2). the slope of a line parallel to the given line is . a point on the line parallel to the given line, passing through (−4, 2), is . the slope of a line perpendicular to the given line is . a point on the line perpendicular to the given line, passing through (−4, 2), is .

a. The slope  of a line parallel to the given line is 1

b. A point on the line parallel to the given line, passing through (−4, 2), is  (1,7)

c. The slope of the line perpendicular to the given line is -1

d. A point on the line perpendicular to the given line, passing through (−4, 2), is (3,-5)

Step-by-step explanation:

The equation of the line in Slope-intercept form  is:

Where m is the slope and b is the y-intercept.

a. For the line

You can identify that:

 By definition, two lines are parallel if they have the same slope. Then, the  slope of a line parallel to the given line is:

b. The equation of the line in Point-slope form is:

Where m is the slope and ()  is a point of the line.

Given the point (-4,2), substitute this point and the slope of the line into the equation:

Give a value to "x", substitute it into this equation and solve for "y":

For :

Then, you get the point (1,7)

c. The slopes of perpendicular lines are negative reciprocals, then the  slope of a line perpendicular to the given line is:

d. Given the point (-4,2), substitute this point and the slope of the line into the equation:

Give a value to "x", substitute it into this equation and solve for "y":

For :

Then, you get the point (3,-5)

step-by-step explanation: so we look at the formula un = a + (n-1)d

un is the amount of seats

n is the nth term aka row number

a is the original sequence/row number

d is the difference between each term

so in this a=22 d=6 and n can remain as n because we are simply formjng a rule

lets put these in the equation

un=22+(n-1)(6)

this is your answer to part a

however

lets double check that this is correct, we'll try putting it into the second term

un=a+(n-1)d

u2=22+(2-1)(6)

u2=22+6

u2=28

as the question said the second row has 28 seats so now we know the formula we made is correct.

as for part b

un=a+(n-1)

its asking us to find a row with 100 seats.

remember un was the amount of seata so all we do is substitute this in.

un=100 a=22 d=6

un=a+(n-1)d

100=22+(n-1)(6)

so now we simplify to find n which is the row number.

100-22=22+(n-1)(6)-22

78=(n-1)(6)

78/6=(n-1)(6)/6

13=n-1

13+1=n-1+1

14=n

so now we know that in the 14th row there is 100 seats.

hope this and that you understood! its my first time using the app or anyone out on here : p its also me to revise so a bunch! ask more questions if you dont understand ☺

in 1995, potato plants were taken into space aboard the space shuttle columbia.

step-by-step explanation: