Question

Please help!
I have an assignment that I have been trying to do but i'm a bit stuck. I have done the first questions but need help on the last ones. Help would be much appreciated. (i will put pictures below)

Answer 1

This is what I have. And I have already done questions 1,2,and 3, but only got halfway on 6&7. I drew the triangle and rectangle but I'm not sure how to get the length of the sides.Im also not sure how to do 4&5. I know that for parallel the slopes are the same and for perpendicular they're opposite reciprocals, but do I have to draw two new lines to accommodate the given points?

Answer 2

to do Q4, we need to know the equation of the line for Q2 (for example)
a parallel line will have the same slope

I don't know what slope you got for Q2, but pretend it was 2.
then the equation for Q4 would be
y = 2x + b
(same slope, but we need to find b)
they say this line goes through the point (1,-3) (i.e. when x is 1, y is -3)
so use that info to get
-3 = 2*1 + b
or
-3 = 2+ b
to find b, add -2 to both sides and simplify

but remember we need the slope for Q2 (which is probably not 2)

Answer 3

for Q5
a perpendicular slope to slope "m" is -1/m
for example if m is 2/3 then the perpendicular slope is -3/2 (flip and negate)
or: -1/2 and 2
or 2 and -1/2
or 3 and -1/3

say you choose the line from Q2. get its slope and "flip it"
then multiply by -1
after you get the slope, it is the same problem as Q4... you have to find b

Answer 4

for Q6, I would pick a "simple triangle" (a right triangle with legs that go straight across and straight up/down) we don't have to, but it is easier.

the length of the straight across line is easy: count the number of squares
(or subtract the x values)

for a slanted line you have to use the distance formula
do you have that in your notes?

Answer 5

I don't know if you have to plot the lines for Q4 or Q5
but it can't hurt. once you have the equation, find two points on the new line and plot them... then connect the dots

Answer 6

THank you so much for helping me! sorry i didnt respond right away! I didnt realize that someone was actually looking at my question. I had given up haha.

Answer 7

try to make progress
if you post your work someone (me? if I'm here) will check it.

Answer 8

okay. for 4 and 5 what do you mean by plot lines?

Answer 9

you wrote
*** but do I have to draw two new lines to accommodate the given points?***

which I assumed meant: do I have to plot the new lines which will be parallel or perpendicular to the original line?

and I thought it would not hurt.

Answer 10

oh okay, I see.

Answer 11

I was going to do the line I drew over the left side of the triangle since its goes through the points it gave me. would that work?

Answer 12

what two points does it go through. I'm not sure which line you mean

Answer 13

one second. Ill show the updated picture

Answer 14

I cut the triangle in half to make it how you said it would be easier.

Answer 15

the line that runs alongside the left side of the triangle

Answer 16

ok, but first we have to fix that line.
it goes through (2,5) and (4,8)
its slope is change in y divided by change in x
(8-5)/(4-2) or 3/2
we can say
y = (3/2)x + b
now use (2,5):
5 = (3/2)*2 + b
5= 3+b
b= 2
and the equation is y= (3/2)x + 2

Answer 17

okay, so where would I go from there

Answer 18

notice, when y= 19 (top of the outer box)
19= (3/2)x + 2
add -2 to both sides
17 = 3/2 x
multiply both sides by 2/3
34/3 = x
or x = 11.333 (11 and 1/3)

not x=12 as you have. in other words your line on the graph is a little off

Answer 19

okay, so would i move it up just a little?

Answer 20

not up. I would move the point at (12,19) to (11 1/3 , 19)
you will have to estimate 1/3 of box over from 11
then redraw the line to go through the 3 points
(2,5), (4,8) and (11 1/3, 19)

Answer 21

Okay. The (4,8) is the lower left part of the rectangle..

Answer 22

ok. after you fix the line we can do Q4

Answer 23

Okay:)

Answer 24

btw, y= (3/2) x + 2
will be an answer for Q2 . a line with positive slope
and you have the work up above on how we found the equation

Answer 25

Q4 ... the question is a bit muddled but I assume it is the new line that goes through (1,-3)
and they want it parallel to
y= (3/2) x + 2

parallel means the same slope.

so write the new equation. can you do that ?

Answer 26

so would it just be y=(1/-3)x+2?

Answer 27

start with
y = m x + b (the "skeleton" that we fill in)

we want this line to be parallel to y= (3/2)x + 2
what slope should we use for m ? (parallel means *same* slope)

Answer 28

okay, so would the (3/2) be the same then?

Answer 29

Q1 is making the graph. you mean Q2 and Q3?

for the "old line" we can use the line you used for Q2
what was it ?

Answer 30

yes, i already did 1,2, and 3

Answer 31

You have to choose 2 locations that make a line and are either positive or negative. I

Answer 32

what did you choose?

Answer 33

i chose (2,5) (12,19) for positive
(21,5) (12,19) for negative.

Answer 34

so for Q4, would it still be y=(3/2) +b

Answer 35

but we still have to find b

Answer 36

if you change to (2,5), (4,8) we will get 3/2 for the slope (a much nicer number than if we use (12,19)

Answer 37

okay

Answer 38

and change (21,5) (12,19) for negative. to (21,5), (19, 8)
(same reason..a nicer slope)

Answer 39

make both of them negative?

Answer 40

no. for Q2 use the points (2,5) and (4,8) (slope will be 3/2)
for Q3 use the points (21,5), (19,8) (slope will be -3/2)

Answer 41

Ohhh okay haha

Answer 42

I hope that gets straightened out.

but for Q4, we want a line parallel to the line from Q1 which has a slope of 3/2
we start with
y= mx + b
we replace m with 3/2
y= (3/2) x + b
we want this new line to go through (1,-3)
replace x and y with those numbers
-3 = (3/2)*1 + b
can you find b ?

Answer 43

would i solve for b

Answer 44

yes. can you do that?

Answer 45

I mean do i isolate it

Answer 46

yes

Answer 47

okay so i got (-3/1)-(3/2)

Answer 48

yes, but people would combine that
either put -3 over the common denominator of 2 (i.e. write it as -6/2 )
or change 3/2 to 1.5 and figure out -3 - 1.5

Answer 49

okay so it would be -4.5?

Answer 50

yes, or -9/2 (same thing)

Answer 51

so the answer for Q4 is y = (3/2) x - 9/2

Answer 52

y=(3/2)*1+(-9/2)?

Answer 53

ok you already said that.

Answer 54

sorry haha

Answer 55

right, sorry

Answer 56

that was disgusting

Answer 57

wow. okay. im sorry you guys had to go through that.

Answer 58

i blocked them

Answer 59

ready for Q5?

let's use the same line with slope (3/2)
and we want a perpendicular line

y= mx + b
any idea what we use for m ?

Answer 60

(-3/2)?

Answer 61

since theyre reciprocals?

Answer 62

we want "flip and negate"
you negated but did not flip

Answer 63

(-2/3)

Answer 64

yes
so we have
y = (-2/3) x + b
and they want this to go through point (-2,7)

Answer 65

to find b, replace x and y with those numbers

Answer 66

okay so it would be 7=(-2/3)*-2+b

Answer 67

yes

Answer 68

then solve for b again right

Answer 69

yes

Answer 70

7/-2- (-2/3)=b

Answer 71

sorry i didnt put parenthesis on the first pair

Answer 72

that looks a bit peculiar.

start with
7=(-2/3)*-2+b

can you do -2 * -2/3
?

Answer 73

(-4/6)?

Answer 74

(4,6)

Answer 75

sorry forgot a negative times a positive for a second. haha

Answer 76

it is
\[ -2 \cdot \frac{-2}{3} = \frac{-2}{1} \cdot \frac{-2}{3}\]
when you multiply fractions you multiply top * top
and bottom * bottom

Answer 77

4/3?

Answer 78

yes.
so you have
7 = 4/3 + b
now add -4/3 to both sides

Answer 79

(7/-2)+(4/3)=b?

Answer 80

wait whoops

Answer 81

hold on, sorry

Answer 82

7+4/3? i was looking at my old equation

Answer 83

close. but added +4/3
we want -4/3 (because on the right side we want 4/3 - 4/3 which cancels)

Answer 84

im sorry, thank you for being so patient with me. math really isnt my stronest subject... at all.

Answer 85

okay, gotcha

Answer 86

so just 7+(-4/3)

Answer 87

b= 7 - 4/3

change 7/1 to 21/3 (multiply top and bottom by 3)

Answer 88

and yes you can write it 7 + (-4/3)

Answer 89

so 25/3?

Answer 90

21/3+4/3=25/3

Answer 91

if you did 21/3 + 4/3
we have 21/3 - 4/3

Answer 92

oh right ints negative

Answer 93

17/3

Answer 94

and the equation is ?