Question

@hartnn @jim_thompson5910 Think you can help me with 2 hard questions?

Answer 1

wut are they?

Answer 2

Consider the equation 7x + 3y = 42.

Part 1: On your own paper, graph this equation using the slope-intercept method. In the space provided, explain, in words, each step of the procedure you used. Make sure to use complete sentences and correct grammar.
Part 2: On your own paper, graph this equation using the intercepts method. In the space provided, explain, in words, each step of the procedure you used. Make sure to use complete sentences and correct grammar.
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Consider the line that passes through the point (-3, 2) and has a slope of 3.

Part 1: Write the equation of this line using point-slope form.
Part 2: Using your equation from part 1, rewrite this equation in slope-intercept form. Make sure to show all of your work.
Part 3: Using your equation from part 2, rewrite this equation in standard form. Make sure to show all of your work.

Answer 3

to do part 1 for 7x + 3y = 42, you need to first solve for y

Answer 4

y is 14, right?

Answer 5

well you're doing the intercepts method, which is part 2

Answer 6

but part 1 wants 7x + 3y = 42 in slope intercept form first

Answer 7

you are correct though, the y-intercept is 14

Answer 8

y = x + 14?

Answer 9

7x + 3y = 42

3y = 42 - 7x

3y = -7x + 42

y = -7x/3 + 42/3

y = -7/3x + 14

so you were close

Answer 10

you forgot to divide the -7x by 3 to get -7/3x

Answer 11

oh yeah i always forget that

Answer 12

so y = -7/3x + 14 tells us that the y-intercept is 14

Answer 13

we start with the point (0,14)

then using the slope, you go down 7 units, then go to the right 3 units to get to the point _____

Answer 14

(3,7) ?

Answer 15

good, you now have 2 points needed to graph this line

Answer 16

the two points are

(0, 14) and (3, 7)

Answer 17

I'm really stumped on part 2.

Answer 18

part 2 is using the method we did beforehand

Answer 19

I'm horrible at the standard way

Answer 20

where you plug in x = 0 to find y

then plug in y = 0 to find x

remember that method?

Answer 21

yes.

Answer 22

that's what you're doing for part 2

Answer 23

okay, can you help on the second one?

Answer 24

sure

Answer 25

point-slope form is this

y - y1 = m(x - x1)

Answer 26

m is the slope

(x1, y1) is the point that the line goes through

Answer 27

we're given

Consider the line that passes through the point (-3, 2) and has a slope of 3.

so the slope is m = 3

the given point it goes through is (-3, 2), so

(x1,y1) = (-3, 2) ----> x1 = -3, y1 = 2

Answer 28

so

y - y1 = m(x - x1)

y - y1 = 3(x - x1) ... plug in the slope

y - 2 = 3(x - (-3)) ... plug in the point the line goes through

y - 2 = 3(x + 3)

Answer 29

and you leave it like that because they want it in point-slope form

Answer 30

Awesome! Thanks.

Answer 31

parts 2 and 3 should be pretty straight forward, if not, let me know

Answer 32

okay, thanks so much :)

Answer 33

yw

Answer 34

Graphing the line using intercepts methods, that should be easy. Let's work on that

Answer 35

7x + 3y = 42

A line with x intercept a and y intercept b is of the form
\[\frac x a +\frac y b=1\]
So, here we'll divide the whole equation by 42
\[\frac{7x}{42}+\frac{3y}{42}=\frac{42}{42}\]
\[\frac{x}{6}+\frac{y}{14}=1\]

Do you understand this?

Answer 36

Somewhat, yes.

Answer 37

So tell me what are the x intercept and y intercept is here?

Answer 38

x- 6 and y-14 ?

Answer 39

Read my second post again

Answer 40

I don't think I understand it. I'm horrible at this form of it.

Answer 41

ash2326, I think when unheard wrote out "x- 6 and y-14" she meant that the x-intercept is 6 and the y-intercept is 14

Answer 42

Is it @unheard ?

Answer 43

Yes, That's what I meant.

Answer 44

I'm sorry, ok let's plot it

Answer 45

x intercept 6
y intercept 14
So we have two points
\[(6, 0), (0, 14)\]
Let's mark these on graph, and then we'll join them to get the line

Answer 46

I have joined the two points with a line, and extended it both the sides. Do you understand this?

Answer 47

Yes

Answer 48

Ok, let's work on the other one

Answer 49

Consider the line that passes through the point (-3, 2) and has a slope of 3.

Point slope form of the equation

It uses the definition of slope, do you know what's slope?

Answer 50

Hold on, I don't know how I would type the other one out.

Answer 51

I'll given you some idea

Answer 52

Steps
1) Divide the whole equation by 42, to get 1 on right side.
2) Simplify the left side to get the intercept form of the equation
3) In the denominator of x is the value of x intercept, mark the point (6, 0) on the graph
4) In the denominator of y is the value of y intercept, mark the point (0, 14) on the graph
5) Join the two points using a line and extend the line both sides to get the required line

Answer 53

Okay, got that down. :)

Answer 54

Ok, so what's slope?

Answer 55

Gah I can't figure it out :(

Answer 56

Slope is change in y over change in x
Suppose you have two points (1, 2) and (3, 5)
\[Slope=\frac{5-2}{3-1}=\frac 32\]
The higher the slope, the steeper will be the line

Do you get some idea?

Answer 57

So 3/2? I can't really tell without the number line, thing. I'm usually better with visuals.

Answer 58

So yes?

Answer 59

Do you get it?

Answer 60

Yes, mostly. It's a bit late so I'm a bit out of it, but I think I get it. I just REALLY need help on 2 + 3 of the second one.

Answer 61

Line passes through the point (-3, 2) and has a slope of 3.
Let's find the point slope form of the line
Let (x, y ) be on the line, other point is (-3, 2)
Writing the slope formula
\[\frac{y-2}{x-(-3)}=3\]
\[\frac{y-2}{x+3}=3\]
This is the slope point form do you get it?

Answer 62

The second one is the point- slope form?

Answer 63

yes

Answer 64

You can cross multiply it
\[y-2=3(x+3)\]