Question

I really don't understand my lesson on lines and slope. (Edit: Can somebody answer the question at the very bottom?)

Answer 1

Could somebody lead me through one problem and then check a second one that I try by myself?

Answer 2

The equation of line CD is y = −2x − 2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4, 5).
y = −2x + 13

y = negative 1 over 2x + 7

y = 1 over 2x + 3

y = − 2x − 3

Answer 3

I would especially appreciate a step by-step explanation of what to do.

Answer 4

A parallel line has the same slope

Plug into the equation y-y1 = m(x-x1)

Answer 5

slope = -2 point (4,5)

y - 5 = -2(x-4)
y-5 = -2x+8
y = -2x + 13 in standard form the line would be 2x+y = 13

Answer 6

Slope intercept form is the y = -2x + 13

Answer 7

ok give me a minute to comprehend that

Answer 8

\(\large \begin{array}{llll}
y = &{\color{red}{ -2}}x − 2\\
&\ \uparrow \\
&slope
\end{array}\)

Answer 9

OK...if you want to do another problem, I'll watch what you do.

Answer 10

^ thank you. @jdoe0001 I don't even know which bits represent what in the equation.

Answer 11

And ok, @DSS . Just one second, thanks

Answer 12

The -2 is the y-intercept...means the line crosses the y-axis at (0,-2)

Answer 13

y = (whatever value here) x + (who knows some other value)
^ ^
slope y-intercept

Answer 14

This is the picture of y = -2x-2

Answer 15

so, you'd want to solve for "y" to get it to look like so first, so you can spot them easily

Answer 16

and is the x the x intercept? or is the x intercept ot used?

Answer 17

*not

Answer 18

y-intercept

Answer 19

the x that you didn't mark is the y intercept?

Answer 20

no, the "x" is part of the equation, but is NEITHER the slope or the y-intercept, the "x" you can say is just along for the ride =)

Answer 21

oh ok

Answer 22

What are the rules about parallel and perpendicular lines? Like doesn't the perpendicular have to flip and turn the numerator negative?

Answer 23

yes

Answer 24

ok
And then parallel stays the same for slope?

Answer 25

http://fooplot.com/#W3sidHlwZSI6MCwiZXEiOiItMngtMiIsImNvbG9yIjoiI0VCMDkwOSJ9LHsidHlwZSI6MCwiZXEiOiItMngrMTMiLCJjb2xvciI6IiMyNzE1RTgifSx7InR5cGUiOjAsImVxIjoiKDEvMil4LTIiLCJjb2xvciI6IiNDODI1REUifSx7InR5cGUiOjAsImVxIjoiKDEvMil4KzEzIiwiY29sb3IiOiIjMjM4QUQ5In0seyJ0eXBlIjoxMDAwLCJ3aW5kb3ciOlsiLTE5LjM5Njk3MjY1NjI0OTk5MyIsIjIwLjI3NTg3ODkwNjI0OTk4NiIsIi03LjM3MzA0Njg3NDk5OTk5NjQiLCIxNy4wNDEwMTU2MjQ5OTk5OSJdfV0-

Answer 26

oh ok wow

Answer 27

the resources I'm provided with always astound me

Answer 28

as you can see, parallel lines have the same slope
perpendicular ones, have "negative reciprocal" slopes

Answer 29

I see

Answer 30

I think I get it? I'll do my other question, could one of y'all tell me whether i get it right or not?

Answer 31

ok

Answer 32

Thank you. It might take a minute.

Answer 33

The bit that you labeled as Y intercept has a fraction in this problem. Why is that?

Answer 34

The equation of line WX is y = −2x − 5. Write an equation of a line perpendicular to line WX in slope-intercept form that contains point (−1, −2).

y = 1 over 2x + 3 over 2

y = negative 1 over 2x + 3 over 2

y = 1 over 2x − 3 over 2

y = − 1 over 2x − 3 over 2

Answer 35

@jdoe0001

Answer 36

well... you know the slope of a perpendicular line to y = −2x − 5, right?

Answer 37

Youd turn -2 into -2/1 and then flip it

Answer 38

but then what bit would be negative?

Answer 39

well... -2 into a +2 and flip it, yes 1/2

Answer 40

oh ok. So you just change whatever the sign was before... so the 2 is positive

Answer 41

pretty much, yes NEGATIVE RECIPROCAL

a
NEGATIVE OF a
-a

RECIPROCAL of that
1/-a

Answer 42

ok

Answer 43

so the slope of the perpendicular line is 1/2?

Answer 44

but wait, I thought it was the 1 that should change signs?

Answer 45

y = −2x − 5
^
slope
-2

negative -(-2) = +2
reciprocal 1/2

Answer 46

oh ok

Answer 47

So how do I know if the y intercept is positive or negative?

Answer 48

now to find the equation of that line, now that we know its slope, well \(\bf \begin{array}{lllll}
&x_1&y_1\\
&({\color{red}{ -1}}\quad ,&{\color{blue}{ -2}})
\end{array}
\\\quad \\

slope = {\color{green}{ m}}= \cfrac{1}{2}
\\ \quad \\

y-y_1={\color{green} m}(x-x_1)\Leftarrow\textit{point-slope form, plug in the values}\\ \quad \\

y-{\color{blue}{ -2}}={\color{green}{ \cfrac{1}{2}}}(x-{\color{red}{ -1}})\)

Answer 49

then, distribute, simplify and solve for "y"

Answer 50

Can i turn y--2 into y+2 ?

Answer 51

Or will that somehow distort the answer?

Answer 52

nope. you ARE expected to multiply them, yes, so y--2 or y-(-2) = y+2, that's correct

Answer 53

ok

Answer 54

I got y+2 =1/2x-1/2 thus far

Answer 55

hmm x-(-1) = x+1

Answer 56

I'm confused

Answer 57

\(\bf y-{\color{blue}{ -2}}={\color{green}{ \cfrac{1}{2}}}(x-{\color{red}{ -1}})\implies y+2= \cfrac{1}{2}(x+1)\)

Answer 58

\(\bf y-({\color{blue}{ -2}})={\color{green}{ \cfrac{1}{2}}}(x-({\color{red}{ -1}}))\implies y+2= \cfrac{1}{2}(x+1)\)

Answer 59

oh no i wrote it down wrong...

Answer 60

y= 1/2 x - 1 1/2?

Answer 61

Which would turn to 3/2

Answer 62

yeap y= 1/2 x - 1 1/2\(\bf \checkmark\)

Answer 63

ok awesome

Answer 64

so that would be d?

Answer 65

oh wait no

Answer 66

slope is positive, so would be "c"

Answer 67

c

Answer 68

lol yeah

Answer 69

ok great

Answer 70

Thank you so much!

Answer 71

yw

Answer 72

And the first question The equation of line CD is y = −2x − 2. Write an equation of a line parallel to line CD in slope-intercept form that contains point (4, 5). was -----> y = −2x + 13 right?

Answer 73

Yep! :)