Question

Which of the following is an equation of a line with a slope of -2 that passes through the point (-4,3)?

I believe the answer is y=-2x-5 but i want to know how to do it.

Also, how do i write an equation of a line that passes through (-2,5) and (1,2)

Answer 1

Since you know the slope is -2 you know the equation is something along the lines of y=-2x+b

Answer 2

yes yes

Answer 3

and since you know it passes (-4,3) you know that the equation should hold true for 3=-2x+b

Answer 4

oh sorry i mean 3=-2*(-4)+b

Answer 5

OHHHH man that makes a lot more sense

Answer 6

you're welcome

Answer 7

the second question is very similar except you have to find the slope first, which is defined by

\[\frac{ \Delta y }{ \Delta x }\]

Answer 8

on the first one i got to 3=8+b then what?

Answer 9

what value should b have so that 8+ b is equal to 3?

Answer 10

in other words by how much is 8 greater or smaller than 3

Answer 11

-5

Answer 12

so b is -5

Answer 13

indeed, so b is equal to -5

Answer 14

correct

Answer 15

ahhhhh

Answer 16

the 2nd one is still confusing

Answer 17

alright, i guess the notation i gave you is not really helpful. I'll try to explain

Answer 18

by defintion the slope is the amount that Y (the vertical axis) increases compared to when X increases by 1.

Answer 19

What did you draw there?

Answer 20

so in the little drawing i made it would be 2 (since they both start at 0 and when x reached 1, y already went to 2)

Answer 21

So basically you drew The equations (-2,5) and (1,2) ?

Answer 22

no that was y=2x except it's not to scale so it's a bit ugly

Answer 23

\[Slope = \frac{ Increase~of~y }{ Increase~of~x }=\frac{ \Delta y }{ \Delta x }\]

Answer 24

that is the definition of slope

Answer 25

is this not y=2x?

Answer 26

I'll use a better program to draw, give me a second

Answer 27

Lol ok sorry im just getting confused

Answer 28

it's ok, it's hard to explain over the internet but i'll do my best to understand it in a simple way

Answer 29

Alright thanks

Answer 30

http://zimmah.webs.com/graph.jpg

Answer 31

as you hopefully can see the y value increases twice as fast as the x value.

Answer 32

ok i suppose i can understand that

Answer 33

Alright, so do you understand the concept that by definition the slope of a graph means the speed that the y value increase compared to the x value (in other words how steep it climbs)?

Answer 34

sure

Answer 35

Alright, and i assume you also are aware that the coordinates are written (x,y)?

Answer 36

yep

Answer 37

so we have \[\large (x_1,y_1)=(-2,5)\]
\[\large (x_2,y_2)=(1,2)\]

Answer 38

and since the slope is chance of y divided by change of x. We can calculate the change of x or \( \Delta x\) by \(\large x_2-x_1 \) while we can calculate the change of y or \( \Delta y\) by \(\large y_2-y_1\)

Answer 39

so in the end we have \[\large Slope = \frac{ \Delta y }{ \Delta x }=\frac{ y_2-y_1 }{ x_2-x_1 }\]

Answer 40

get that?