I need help with slopes!?

Question

I really need help in math. i feel like im dumb and i dont understand as much as the other kids but i wish i did. our teacher doesnt really do a good job of teaching us and when i ask her to explain she explains it in a completely different way than the way she explained it before.
Anyways im in 8th grade and i dont know ANYTHING about slopes. its really frustrating to look in my folder and see homework papers with no work on them because i dont understand how to do it.
were working on slopes, is there any STEP BY STEP CLEAR WAY to explain how to do slopes and solve any slope equation?
and CLEAR STEP BY STEP INSTRUCTIONS on how to:
write an equation in standard form:
examples: 2x= -5 + 11 and 4x - 7y + 15 = 10

2. how to find the x and y intercepts for each equation
example: x+y=5 ( i know that sounds really dumb prob because i am)
4x - 3y = 12

and any tips, tricks, suggestions ANYTHING on slopes please im begging i just really want to be smart or smarter at least i dont want to be the dumb kid left behind all the time!

Answer 1

If you THINK you are dumb, then you most certainly are. Your view of yourself is what "makes" you dumb. Once you think, "I can't do that", you are usually correct. The correct view is, "I CAN do this. I might have a bit of trouble, but I CAN do it." You know something??? You CAN.



Most of math is quite easy, once you understand the basics. Most folks have trouble in mathematics because they try to study it like english or history. If you are reading more than 3 pages an hour in mathematics, you are reading too fast. In college, I had 7 psych texts, 5 history texts, and 4 speech texts, and 1 math text my first semester. That 1 text was used for FOUR math courses. It should take you AT LEAST 30 min to read what I have written.



But to your problem. You have asked several questions, and I don't know how much room I have.



email me and I'll give you more help.



Slope.



This is merely how much of a unit (1) change in one variable produces in another. You earn $5/hr. That means for every hour you work, you earn $5. The slope of the equation is "5". It might look something like this:



amount earned = 5 x hours



Now, suppose you get an extra $10 bonus just for showing up.

Well, now the equation might look like:



amount earned = 5 x hours + 10 bonus



however, we tend to use general terms in mathematics, so we'll write it a bit differently.



y = 5x + 10



Now, suppose Johnny can run 100 years in 25 seconds? How far wil he run in 1 sec. Well, lessee, 100/25 = 4, must be 4. You know, "4" is the "slope", since it states how far he will go for each second.



Now, in terms of (x, y), you have two points, say (4, 8), (7, 20). (draw a pic if you can).

if we subtract the y points 12 and 8, we get the distance "up".

If we subtract the x points 6 and 4, we get the distance across.

in this case whatever we are working with moves 20 - 8 = 12 in a distance of 7 - 4 = 3.



Now, if something moves 12 in 3, it must be 12/3 = 4/1 so it must have a slope of 4.

HEY, waitaminnit. THAT'S JUST THE FRACTION I LEARNED ABOUT IN THE

FOURTH GRADE!!! It's also the "how far can johnny run" problem.



intercepts.



Ain't it nice how mathematicians confuse things? We give lots of names to the same thing so others will think we are smart. Let us look at the concept of "intercept". That's just the place where a line crosses an axis (either x or y). Not surprisingly, if it crosses the x axis at some point, we call it the "x intercept"; and, of course, where it crosses the y axis, we call it the y intercept.



Now, what do it mean to "cross the y axis"??? Well, it simply means that the value of "x" at that point is zero. Similar with the x axis--the value of y is zero. Now, you know that the equation and graph are "identical". so draw a pic of x + 2y = 8.



To find the "y intercept", we plug in 0 for x to get the equation:



x + 2y = 8; 0 + 2y = 8; or 2y = 8; or y = 4; y intercept at (0, 4) tuff, ain't it???



To find the "x intercept", we plug in 0 for y to get the equation



x + 2y = 8; x + 2(0) = 8; x = 8; x intercept at (8,0)



Standard form of an equation is: ax + by = c, where a, b, c, are integers (no fractions/decimals)

Thus:



2x + 3y = 7 is standard form



2x = y + 3 is NOT. We can subtract "y" from both sides of the equation to get:



2x - y = y - y + 3; combining the y's on the right: 2x - y = 3 is NOW in "standard form"



consider your examples: 2x= -5 + 11 and 4x - 7y + 15 = 10



the second one is "easy", just subtract 15 from both sides to get 4x - 7y = -15



The first one is "tricky" because you did not copy it correctly.



2x = -5 + 11; ==> 2x = 6 ==> 2x + 0y = 6



write if you need more help



always,

tony

Answer 2

This is long, but I'll be clear as best as I can. Hope you follow.



Standard Form: Ax + By + C = 0 (A, B, C are simply just constants)

So, for your example: 4x - 7y + 15 = 10, to put this into standard form, simply subtract 10 on both sides and your equation is now: 4x - 7y + 5 = 0



I am going to use this equation: 4x - 7y + 5 = 0 as an example



To find slope, transform the equation to isolate y (y = ...); this is called slope-intercept form

So, for: 4x - 7y + 5 = 0, solve for y



4x - 7y + 5 = 0

-7y = -5 - 4x

7y = 5 + 4x

y = 5/7 + (4/7)x



y = (4/7)x + 5/7



4/7 is your slope



y = mx + b is slope-intercept form, where m is your slope and b is your intercept



For drawing the graph of the equation:

Intercept simply means the initial change in the graph in the y direction. Think of this, in a graph, you start out at (0, 0). In the example above, + 5/7 means you first move up to (0, 5/7). The slope is m. Slope "m" means rise over run (rise/run). The slope in the example is 4/7 = rise/run. So, from (0, 5/7), you move up 4, then move right 7. It will be easier if the numbers were whole numbers, and not fractions. Let's say the slope was -4/7, this simply means you vertically go down 4 BUT still move right 7.



These are important formulas that you basically have to memorize:



y = mx + b (basically transform the given equation to this form), where m is slope and b means intercept



slope = m = (y2 - y1)/(x2 - x1)

Use this formula if you are given to ordered pairs. This formula will help you get your slope, m. So, for example, let's say you're teacher gives you to random ordered pairs: (4, 2) and (5, 6). Your teacher asks you to find the slope. This is what you do:



So, you have (4, 2) and (5, 6)

4 is your first x (x1)

2 is your first y (y1)



5 is your second x (x2)

6 is your second y (y2)



slope = m = (y2 - y1)/(x2 - x1)

Just substitute

m = (6 - 2)/(5 - 4) = 4/1 = 4

4 is your slope



Another useful formula to memorize is y - y1 = m(x - x1)

This formula is used to find your equation if you just given two ordered pairs (like the little example above). This formula is called point-slope formula



From the example above, the two ordered pairs you were given was (4, 2) and (5, 6).

To use the point-slope formula to find your equation, first you find the slope (which we did using the slope formula) and then use this point-slope formula to find the equation.



So from the slope formula, we got 4 as the slope. Now, substitute this into the point-slope formula:

y - y1 = m(x- x1)

y - y1 = 4(x-x1)



Now, simply substitute the x1 and y1 value to this equation (Note: You can also use x2 and y2 BUT YOU CANNOT cross match like x1 and y2 and vice versa)



x1 = 4

y1 = 2



y - y1 = 4(x-x1)

y - 2 = 4(x-4)

y - 2 = 4x - 16

y = 4x - 14



So this is your equation. If you want to graph this equation, this is what you do: first take note of the intercept, which is -14. So start your graph at (0, 0) and move vertically down 14. Your graph is now at (0, -14). Think of your intercept meaning as your starting point of your graph. Next plot the slope. Your slope is 4, which means rise (move up) 4 and run (move to the right) 1.



INTRO TO X AND Y INTERCEPTS:

x-intercept is the value of x when y equals 0

y-intercept is the value of y when x equals 0



For your example, x + y = 5:



x-intercept = the value of x when y is 0

Substitute y to 0

x + 0 = 5

x = 5

So your x intercept is 5



Finding y intercept (the value of y when x is 0), substitute x to 0

x + y = 5

0 + y = 5

y-intercept is 5



For your other example, 4x - 3y = 12

The x-intercept should be 3

The y-intercept should be -4



GOOD LUCK

Answer 3

What i learned is that a function is basically a function that is in the shape of a line. The function is y=mx+b. The x value is the independent variable, and the y value is the dependent variable. One y value will not take on 2 x values.



An example is that y=2x+5 is a function, and if you gave in a random number for x, like 5, then the y would be 15. So you would plot that on the graph: 5 for x, 15 for y. Inversely you can find the x if you are given y=15 and not x=5.



For your example: 4x-7y+15=10, THE NUMBERS THAT YOU MOVE TO THE OPPOSITE SIDES WILL BE MULTIPLIED BY -1.



so 4x-7y+15=10

let's keep the y's on the left, x's and others on the right.

-7y=10-4x-15 you move the 4x and the 15, they are both multiplied and become negative numbers.

y=(10-4x-15)/(-7) the rule is that if you divide one side by a number, you have to divide the other side too. Same rule if you want to multiply both sides. Here we divide each side by -7.



2. the intercepts are the values that will touch the graph on the x and y lines.

so for x+y=5 to find the value that y is when the line touches the graph, you give x=0.

so 0+y=5

y=5 coordinates (0.5)

to find the value that x is when the line touches the graph, you give y=0

so x+0=5

y=5 coordinates (5,0)