Question

Write an equation in point-slope form that fits the description given.

1) contains the point (5,8) and is parallel to y = 5x + 12

2) contains the point (6,1) and is perpendicular to y = 3x - 22

3) contains the point (2,5) and is parallel to y = 8x + 10

Answer 1

What is the correlation b/w parallel lines and the slope? b/w perpendicular lines and the slope?

Answer 2

For each one:
1. Find the slope of the given line
2. based on what type of line you are looking for - what is the slope of the new line
3. use point slope form to find the new line

y - y1 = m(x - x1)
plug in your point of x1,y1
and new slope for m

rewrite this into y = mx + b format

Answer 3

you catch all that?

Answer 4

It's a bit confusing for me

Answer 5

i didn't think so

1) contains the point (5,8) and is parallel to y = 5x + 12

Answer 6

the " parallel to y = 5x + 12 " says the slope is the same as the slope of \(y=5x+12\) which looks just like \(y=mx+b\) a line with slope \(m\)
so your slope is \(5\)

Answer 7

I didn't think I was too convoluted.

Answer 8

Do you understand the correlation b.w slope and types of lines...that is very important, hence my first question. But you are in good hands! Happy studying

Answer 9

the slope is 5, the point is \((5,8)\) write it as
\[y-y_1=m(x-x_1)\]with
\[m=5, x_1=5,y_1=8\] you get
\[y-8=5(x-5)\]

Answer 10

I'm not sure about the correlation but I'll try to figure it out thanks

Answer 11

@JuanitaM it was not at all convoluted, but the steps may not be clear

Answer 12

Yeah, It didn't sound clear to me thats why

Answer 13

you good from \[y-8=5(x-5)\] because you are still not done

Answer 14

Yeah, I got y−8=5(x−5)

Answer 15

i mean after that?

Answer 16

steps are always the same
multiply out on the right using the distributive law
\[y-8=5x-25\] then add \(8\) to get
\[y=5x-17\]

Answer 17

Alright, thanks. Working on it right now

Answer 18

2) contains the point (6,1) and is perpendicular to y = 3x - 22

Answer 19

perpendicular to y = 3x - 22 tells you it is perpendicular to a line with slope \(3\)
that means the slope of your line is the "negative reciprocal" i.e
\[-\frac{1}{3}\]

Answer 20

actually, you can stop at
y−8=5(x−5), which is already in point-slope form

if you go further,y=5x-17, this is slope-intercept form

Answer 21

So I can just stop at y - 8 = 5 (x-5) ?

Answer 22

if it says "point slope" then yes, stop

Answer 23

similarly
\[y-1=-\frac{1}{3}(x-6)\] for the second one