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Group Name: idk, Concept 1: How to graph a line By: Karam, Concept 2: How…
Group Name: idk
Concept 1: How to graph a line By: Karam
Using table of values
Using a table of values can help with graphing a line and can also help with what points you will use in the table. In order to do this you need to choose a couple of x values and seal those values into the equation to find the alike y-values of the coordinate point. An example of a table of values for the equation is y= 3x + 2.
https://youtu.be/-u55GD_sGLA
y=mx+b
The last method for this concept is how to graph a line for y=mx+b. Y=mx+b has letters with meaning. The m is the slope and b is the y intercept value. In order to do this method, the first step you need to do is to start plotting the intercept. Keep in mind the y intercept is where the line will cross the y-axis.
Using 1 point and a slope
The third method to graph a line is Using 1 point and a slope. With this method you need to be able to do Rise over Rise as the first thing you need to do is plot the point that is given then us slope formula to do rise over run. At the starting of your point you need count the rise and run to mark the second point. Lastly, connect the points with a line. As a demonstration, I was using this method, so I followed the instructions given and I plotted the first point and did rise/run then counted the numbers and I got 5/6. After that I connected my second point and connecting the two points creating a line on the fourth quadrant.
https://www.youtube.com/watch?v=lkRyxnqOb8M
https://www.youtube.com/watch?v=u3spOO-m_Gg
The slope (m) can figure out the direction of the line varying from positive, negative, zero and undefined. The y-intercept (b) is where the line cuts the y axis.
Using Two points
Using two points is a great second method to graph a line. In order to do this method correctly you the need follow a few important steps. Step number one is to find the slope from 2 points. The second step is to us slope formula. To do slope formula you need to pick one to be x1, y1 and the other to be x2 and y2. After this you need to use the slope equation to calculate the slope. To give an example, we can have (7,8), (5,3). We will subtract 8-3 and 7 and 5. Our final answer will be 5/2.
https://youtu.be/9YQn2NRTnCQ
Concept 2: How to find the slope of a line By: Adam
Using Rise/Run
A way you can find the slope of a given line is by using rise/run. To do this you must first get any 2 points on the line. Rise means how many units you move up or down from point to point. On the graph that would be a change in the y values. Run means how far left or right you move from point to point. After finding those you put it as a fraction in rise/run. Meaning you put your y value over your x.
Depending on whether your slope is positive or negative your rise will be different. What I mean is if your slope is negative your rise will be a negative number and if positive it will be a positive number. If your slopes line is zero that means your slope is zero. If you have an undefined slope your slope is undefined.
https://youtu.be/R948Tsyq4vA
Using Slope formula
In order to find the slope of a line using the slope formula you must get the coordinates of any two points once that's done, it doesn't matter which you pick but you should pick one of the points to be x1/y1 and the other to be x2/y2. After doing that you subract the y2 and y1 and that would be your numerator, and then subtract your x2 by your x1 which would make it your denominator. And that's your slope.
https://www.youtube.com/watch?v=_f_EcNNhXjI
Using y=mx+b
How can you find the slope of a line using y=mx+b? Well when this question comes up they would give you an equation to find the slope and an example would be, y=-2x+6. When something like this comes up its easy as the slope is right there (-2). However some equations will require more work. For example, 2x-7y=10. In an equation like this you must get the y to the left side by itself. After that you isolate it by dividing whatever number is with it in our case that would be dividing by -7 on both sides to all numbers. That would give you your y=mx+b format and your answer.
https://www.youtube.com/watch?v=tonrg08NILk
The equation of a line is mainly written as the form of y=mx+b.
Concept 3: How to use y=mx+b By: Karam
With the horizontal and vertical Lines
For using y=mx+b the equation of a horizontal line passing through a, b is of the form of y=b. On the other hand a vertical line passing through a, b is of the form x=a. To use it you need at least the y-intercept value b which reveals to you where a point of the line is.
In shorter terms
Y=mx+b can be written as y=x. This is because when given y=x this means that y and x values are the same which creates a straight line (linear equation). When this straight line is form its giving you easy knowledge on what the slope (m) is and what the y intercept value (b) is because these can be figured out using this line. A linear equation is an equation between two variables that gives a straight line when it's plotted on a graph.
With a linear equation
https://youtu.be/YJy2m30LqiY
To use y=mx+b with a linear equation y=mx+b is actually the representation of a linear equation meaning that when given a linear equation in order to use y=mx+b you put the slope in replace of the m and the value that the line crosses over the y intercept as b. When this is done your equation can look something like this as an example, y=-4x+10.
Concept 4: How to write the equation of a line By: Adam
When given the slope and y-intercept
When the slope and y-intercept are given its a pretty simple process to do in order to write the equation. What to do is to use the y=mx+b formula. To do this lets say your given slope is 3 and your given y intercept is 15. You would then replace 3 with m because m is what represents the slope, making the equation y=3x+b. And then replacing the 15 with b because b represents the y-intercept value, and your final equation would be, y=3x+15. This equation can also be a bit different as if you have the x and y. When you have it you can substitute it for the x and y variables for lets say that your x is 5 and y is 7 your full equation could be, 7=3(5)+15 (just an example).
https://www.youtube.com/watch?v=oG19cFGRFeA
When given a graph
When given a graph in order to use the equation you must gather all required information such as the slope, y intercept, etc. To do this using a graph unlike when they are just given to you, you need to get two points on your line then figure out the slope either using the slope formula, or rise/run. After doing that you look and determine what value your line crosses on the y intercept. and then put it in the y=mx+b, m being the slope and b being the y intercept value and the x and y corrdinates.
https://www.youtube.com/watch?v=8TIzQ_16q6w
When 2 points are given
When two points are given you must figure out the slope and y intercept value using it. To do this you must use rise over run or the slope intercept formula. Since the 2 points are already given you already know the coordinates and can easily see where the line crosses the y axis and subtract the y values (y2,y1) and the x values (x2,x1)(if you are using slope formula.)
https://www.youtube.com/watch?v=4vXqMsvPSv4
Linear Equations Mind map
Group Members: Karam and Adam
