Question

When there are 30 girls in a dance, there are 12 boys in the dance. When there are 45 girls in the dance, there are 17 boys in the dance. Assume the relationship is linear.

Which equation models the relationship between the number of girls, x, and the number of boys, y?
y = 3x + 26
y=1/2x+22
y=1/3x+2
y=3x+9

Answer 1

x = #girls
y = # boys

they give you two points on the line
(x,y) = (30,12)
(x1,y1) = ( 45,17)

calculate the slope from those 2 points first

Answer 2

Then use one of the points in the slope-point formula for a line

y - y1 = m*(x-x1)

to get your equation for the line

Answer 3

oh i was doing it all wrong i was plugging those in for x and y

Answer 4

nah, those are each a point on the line

Answer 5

whats the formula for finding the slope?

Answer 6

Given 2 points above (x,y) and (x1,y1)

\[slope =m=\frac{ \Delta y }{ \Delta x }= \frac{ y-y1 }{ x-x1 }\]

Answer 7

ok so i plug those numbers into this formula?

Answer 8

Right, it is just the difference in the y coordinate , divided by, the difference in the x coordinate

Answer 9

ok im gonna try to solve it

Answer 10

how exactly do i plot for y1 like do i put the number and 1?

Answer 11

\[y1 = y _{1}\]

just a different y value, was lazy to write the subscript

Answer 12

oooooh ok its ok thanks

Answer 13

What are you getting as the slope?

Answer 14

great work guys u can be the best in ur class

Answer 15

thank you noland

Answer 16

(x,y) = (30,12)
(x1,y1) = ( 45,17)

you getting the slope?

m = (17 - 12) / (45 - 30) =

Answer 17

yes im working on the problem right now and i was doing it wrong

Answer 18

what did you do?

Answer 19

you will get teh same slope if you do it the other way,

m = (12 - 17) / ( 30 - 45)

Answer 20

how r u guys doing so far?

Answer 21

i did 12/30 =12-12(1)
30-30(1)

Answer 22

(x,y) = (30,12)
(x1,y1) = ( 45,17)

\[m = \frac{ y-y1 }{ x-x1 } = \frac{ 12 - 17 }{ 30-45 } = \frac{ -5 }{ -15 } = \frac{ 1 }{ 3 }\]

Answer 23

for (12-17) i got -5 and for (30-45) i got -15

Answer 24

yep, then reduce that fraction like above, to 1/3 by dividing both top and bottom by -5

Answer 25

Now that you have the slope;
m = 1/3
and point on the line
(x1,y1) = ( 45,17)

Use

y - y1 = m*(x-x1)

to form an equation for the line

Answer 26

ok why do we divide -5 into it?

Answer 27

reduce the fraction -5/-15 = 1 / 3

Answer 28

oh ok

Answer 29

now just sub into the point-slope form

y - y1 = m*(x-x1)

using slope m = 1/3 and any of the two points

Answer 30

m = 1/3
(x1,y1) = (45,17)

y - y1 = m*(x-x1)

y - 17 = (1/3)*(x - 45)

Answer 31

ok im getting why i cant do this im not plugging them in right sorry if this may be fustrating for you

Answer 32

now just have to solve that for y = ....

y - 17 = (1/3)*(x - 45)

y - 17 = 1/3 x - 15

y = 1/3 x + 2

Answer 33

nah, you are learning

Answer 34

thank you alot!

Answer 35

if you have another example you want to go through, you can tag me in it

Answer 36

ok i will if i find one i fanned you aswell

Answer 37

i would go back through this thread, and write on paper what i typed in, it may make more sense

Answer 38

ok i will i think that will help me if i ever see a problem like this again

Answer 39

yep, just have to realize the problem is giving you 2 points, from there you just find the slope, and use point-slope form to make a line

Answer 40

ok thanks again truely grateful