Question

Someone please help, even if just for one of them!
1.Write the equation of the line with a slope of -5 and a y-intercept of (0,3).
2.Write the equation of the line with a slope of -1/3 and passing through the point (6, -4).
3.Write the equation of the line passing through the points (0, -4) and (-2, 2).
4.Write the equation of the line passing through the points (-6,1) and (-4,2).
5.Write the equation of the line with an undefined slope, passing through the point (2, 5).

Answer 1

how far did you get?

Answer 2

I don't know how to start

Answer 3

let's start with #1

Answer 4

1.Write the equation of the line with a slope of -5 and a y-intercept of (0,3).

Answer 5

The given slope is -5, so m = -5 (m is the slope)

the y-intercept is (0,3) or just 3, so b = 3

Answer 6

y = mx + b ... start with slope intercept form

y = -5x + b ... replace m with -5 (since m = -5)

y = -5x + 3 ... replace b with 3 (since b = 3)

Answer 7

so the equation with a slope of -5 and a y-intercept of (0,3) is y = -5x+3

Answer 8

make sense?

Answer 9

Okay thank you! so do you use the same formula for all of them?

Answer 10

yes, but the ones that don't have a given slope, you need to find it first

Answer 11

and if you don't know the intercept, you need to find that as well

Answer 12

once you know the slope and y-intercept, you know the equation based on what is done above

Answer 13

okay so what if they give me a line on a graph and tell me to write the equation?

Answer 14

identify two points on that line

find the slope using those two points

then use one of those points (along with the slope) to find the y-intercept

Answer 15

to make life easier, you can visually look for the y-intercept so you don't have to do much work

Answer 16

does that make sense?

Answer 17

kind of

Answer 18

what are two points on that line?

Answer 19

-1 and 3

Answer 20

write them as ordered pairs

for instance, the point (3,1) is on the line (see attached image)

Answer 21

what other point is on the line?

Answer 22

(-3,-3)

Answer 23

good

Answer 24

now use these 2 points to find the slope

Answer 25

you do so by using the slope formula

\[\large m = \frac{y_{2}-y_{1}}{x_{2}-x_{1}}\]

Answer 26

okay!

Answer 27

tell me what you get

Answer 28

,m = -3-1/-3-3

Answer 29

keep going

Answer 30

-2

Answer 31

no

Answer 32

-3 - 1 is equal to ???

Answer 33

-4 /-6

Answer 34

reduce that

Answer 35

-2/-3

Answer 36

keep going

Answer 37

two negatives divide to get a _____

Answer 38

positive

Answer 39

so the slope is 2/3

Answer 40

so given any two points, you can find the slope of the line through those two points (using the slope formula)

so you'll be using this formula for #3 and #4

Answer 41

we now have a slope of 2/3, so m = 2/3

Answer 42

how do we find the y-intercept? ie how do we find the value of b?

Answer 43

i dont know

Answer 44

remember we have the general equation y = mx+b

Answer 45

we know the slope is m = 2/3

we also know that the point (-3,-3) is on the line

so this means that x = -3 and y = -3

Answer 46

plug all this in, then solve for b

\[\large y = mx+b\]


\[\large y = \frac{2}{3}x+b\]


\[\large -3 = \frac{2}{3}(-3)+b\]


\[\large -3 = \frac{2}{3}*\frac{-3}{1}+b\]


\[\large -3 = \frac{2*(-3)}{3*1}+b\]


\[\large -3 = \frac{-6}{3}+b\]


\[\large -3 = -2+b\]


\[\large b = ???\]

Answer 47

-5?

Answer 48

no

Answer 49

you have to add 2 to both sides to isolate b

Answer 50

oh crao i added them, it would be -1

Answer 51

good, look at the graph and notice where it crosses the y axis

Answer 52

oh wow thats alot easier hah

Answer 53

yes BUT you won't always have the graph so it helps to know how to do this without a graph

Answer 54

besides, the line may intersect the y-axis at some point that's not a whole number

Answer 55

anyways, we know the slope is 2/3

the y-intercept is -1

so this means

m = 2/3
b = -1

Answer 56

Now plug these pieces of info in


\[\large y = mx+b\]

\[\large y = \frac{2}{3}x+b\]

\[\large y = \frac{2}{3}x+(-1)\]

\[\large y = \frac{2}{3}x-1\]


So the equation of the line is \[\large y = \frac{2}{3}x-1\]

Answer 57

thank you !

Answer 58

you're welcome