Those Good At Math Can Someone Help With This... Slope Linear Equations?

[meetkitty123]

HELP WITH THE ABOVE PLEASE!

My child is struggling with the above and I will admit im tripped up on the fractions.

I have figured this out down below

So I can do that and explain it to my child but when fractions are mixed with it im stumped.

I took out a bunch of books from the library to help child

But my kid has a test coming up soon and though Im taking a crash self course I could use any and all extra help... Any help please.

[abc3643]

OK, I am going to answer the graphing question based on the top picture.

Here's what you do...

1. Notice that the graph paper has a horizontal X-axis and a vertical Y-axis and where they intersect, that's called "The Origin" and you often see an O or 0 at the intersection.

Here's an example, but without the O.

2. Let's do the one labeled F together... But, first, since I can't write a fraction like it appears in the picture, I am going to have to use parentheses around the fraction. So, for that one labeled F, I'll write:
y = (4/3) x + 16

We generally write these in the form:
y = m * x + b

where:
m is the "slope"; more on that in a moment
b is the "y-intercept", the place on the Y-axis where the line will cross.

The slope is like the angle of the line. The nice thing about slopes being fractions is that they tell you exactly how to easily draw the line.

OK, back to that F equation:
y = (4/3) x + 7

Here, the slope is the number in parentheses, 4/3 and the y-intercept is the 7.
So, we know that our line is going to cross the Y-axis at y = 7. Draw a point on the Y-axis at -7. We identify points as (x, y) so this point would be (0, 7) because the Y-axis is where x = 0.

OK, now here's the fun part... We are going to locate the next point and the slope is going to help us with that.

We know that the slope is 4/3 but this is what's great:
The numerator in this fraction is the top part, so it's 4.
The denominator in this fraction is the bottom part, so it's 3.
Think of the numerator as telling you how many boxes up you are going to go.
Think of the denominator as telling you how many boxes to the right you are going to go.

So, let's draw the next point:
We are starting at (0, 7).
From there, count 4 boxes up, then 3 boxes to the right.
That's going to be at (3, 11) so that's 3 on the X-axis and 11 on the Y-axis.
Draw a dot there.
How did I get that (3, 11)?
The y-intercept was at (0, 7).
By "going 4 boxes up" that means we add 4 to the value of the intercept:
7 + 4 = 11.
By "going 3 boxes to the right" that means we add 3 to the value of x. Since at the intercept, x = 0, that means:
0 + 3 = 3

Now that you have these two points (0, 7) and (3, 11), take a straight edge and draw a line.

3. Let's talk more about slope...
When the slope is positive (that is, greater than 0), the y value increases as you increase the value of x. When the slope is negative (that is, less than 0), the y value decreases as you increase the value of x.

When the slope is written like a fraction like it is in this assignment, that says when making the next point...
The numerator is for telling us how many boxes over vertically we go and the denominator tells us how many boxes horizontally we go.
If the numerator is positive (greater than 0), then we go up; if the numerator is negative (less than 0), we go down.
If the denominator is positive, then we go to the right; if the denominator is negative, we go to the left.

4. Let's now do one with a negative slope. I won't have space to give all the gory details, so I'll make this brief:

The equation labeled K is:
y = (-2/5) x - 6

So, the slope, m, is -2/5 and the y-intercept , b, is -6.

So, we draw the first point which is where the line crosses the Y-axis (which is where x = 0).
That point is (0, -6).

The next point we need the slope. However, this slope is negative; it is less than zero.
So we can think of it like this:
Numerator = -2, Denominator = 5
or
Numerator = 2, Denominator = -5
It's easier to just go with the minus sign being with the numerator.
So, in this problem, the numerator being -2 means our next point will be 2 boxes down and the denominator being 5 tells us our next point will be 5 boxes to the right.
So, the next point is 2 boxes down from (0, -6) and 5 boxes to the right of (0, -6).
Where is that?
x: 0 + 5 = 5
y: -6 - 2 = -8
So, our next point is (5, -8) so draw a point there.

Now that we have our two points:
(0, -6)
(5, -8)
we just use a straight edge to draw a straight line that goes through these two points.

5. In equation E:
y = x - 23
the slope is 1 which you can think of as 1/1 so you go 1 box up and 1 box to the right for your next point.
Thus, the two points to draw are (0, -23) and (1, -22).

6. In equation C:
y = -x + 10
the slope is -1 which you can think of as -1/1 so you go 1 box down and 1 box to the right for your next point.
Thus, the two points to draw are (0, 10) and (1, 9).

I think you can do the rest...

[abc3643]

Oops slight boo-boo in the beginning:

2. Let's do the one labeled F together... But, first, since I can't write a fraction like it appears in the picture, I am going to have to use parentheses around the fraction. So, for that one labeled F, I'll write:
y = (4/3) x + 7

[abc3643]

Here's a quick way to think of this:

The general form is y = m * x + b.
In these problems, m is a fraction, so we have:
m = (m_numerator / m_denominator).

The first point to draw is:
(0, b)

The second point to draw is:
(0 + m_denominator, b + m_numerator)

So let's do Equation L:
y = (-3/2) x - 22

b = -22
m = -3/2
So,
m_numerator = -3
m_denominator = 2

So, the first point to draw is:
(0, b)
which is (0, -22).

For the second point to draw, we plug into:
(0 + m_denominator, b + m_numerator)
to get:
(0 + 2, -22 + -3) = (2, -25)

So, you draw a point at (0, -22) and (2, -25), then use a straight edge to draw a straight line that goes through those two points.

[BeMuse]

They want you to graph the equations. The questions are in slope intercept form y=mx+b where the slope of the line is m, the y coordinate of the y intercept is b. So for example A, the slope is -2/3 and the y intercept is at (0, -16). Slope is rise over run. So when graphing you will go down two and to the right 3 on the graph starting at point (0, -16) on an x/y coordinate plane.

[meetkitty123]

Thank you
So would y= -1/2x - 23 Be y intercept at (0,-23) go down 1 and go right 2 while starting at (0,-23) ?

[BeMuse]

Yep, you're catching on. Rise/Run. If the the rise is positive you go upward. If the rise is negative you go downward.

[meetkitty123]

Got it thank you
Y=-x -23 is y= either or -1/1 or 1/-1 (both are the same) but because it fits better on the graph I will go with y = 1/-1x +10
B= 1/-1(0)+10 = (0,10) as the y intercept
(Starting at 10) using 1/-1 for m or slope I would go up 1 and then to the left 1 and according to this zombie math graphing game I just killed another zombie lol 🤣

[Astarlessnightsky]

You have to choose a value for x and get the corresponding y.

On the second stage it looks like you did it, you inserted the pairs behind the equation and figured out which pairs work and which don't.

On the top sheet, i would assume you draw the graph.
As its a linear graph you only need 2 points of reference, either by choosing 2 values for x and get 2 y values, eg x=1 and x=2.

Or you can use the factor multiplying with x and the /- value at the end.

The /- value (in germany its called b) is the point where the graph meets the y-axis

eg y=x 2 would be 2 on the y axis

and the factor infront of x as the second point. (we called it m)

eg y=2x 2 would be 2 on the y axis and from this you would go one to the right and 2 up for your second point.

or y=⅓x 4 would be 4 on y axis, and 3 to the right and 1 up.

or if you got a negative factor, you would go down.

[Daniela1982]

Taht should be easy. What kid of car do you drive?

[Still-alive]

[OnTheLevel]

The slope of the line is simply the coefficient of the X term. The intercept of the Y-axis is the constant term.

[TallAnon]

Just a quick tip here

[Bklynbadboy12]

I'll do it for you but I want a chat session in return for my knowledge 🤣🤣😉

[GoodGuyBreakingBad]

Sorry I can't help you out, All I took in School was General Math.

[shortster]

The slope or m is the number in front of x.

[shortster]

I used to be an algebra tutor; so if you have any more questions or need more details. I would be happy to help.

[meetkitty123]

I understand what Is "M" what I didn't understand was what to do with the fraction

[shortster]

Just think of it like any other number.

[roy_ricky09]

Oh boy. Good old days.

[jimmy2]

a I think