What is a linear relations

A linear relation is the relation between a variable and a constant. You can show the relationship between the variable and the constant by either graphing it or using a t-chart.  A linear pattern is when there is a constant difference and a non-linear pattern is when there is no constant difference. This meaning that the rule is the same for linear patterns but for patterns the rule can change throughout the t-chart. 

How to find the rule for a pattern

So the first thing I like to do when finding the rule for a patter is to put everything into a t-chart. Next I look at the x side of the t-chart to see if all the numbers are in order. Then, I look at the y side and see how much the number goes up when it comes out. So here it looks like it goes up by 2 the first time but when I reach the end, it seems to go up by 4. So now we have to find the rule they used to get the output. So from what I ca see x had to multiply by 2 and then since that doesn’t give us our y we have to add 1 to get the rule. So we would write this as 2x+1=y or y= 2x+1 they mean the same thing. To tell if the pattern is increasing or decreasing is by one of two things: one you can simply look at the y side on t-chart to see if the numbers are increasing or, you can look at the number the x is being multiplied by to see if the number is going to be increasing or decreasing. 

T-chart – what it is, how to fill it

T-charting is very simple and very easy to understand. So think of the letter T. Now, on the left side we put an X and on the right side we put a Y. Next on the X side we put numbers 1, 2, 3. The numbers don’t have to start with 1 2 3, but it is easier that doing 1001, 1002, 1003. And then using the rule we can calculate the Y side. When you get all three answers, simply put them on the right side matching up with the X. 

How to plot a point (coordinate)

Plotting a point is probably my favorite thing because it is the easiest thing to do. So you take your coordinate. Example: (3,1) The 3 is meaning X and the 1 is meaning Y. X is always horizontal and Y is always vertical. So, next we have to place the coordinate in the right quadrant. There are 4 quadrants going counterclockwise. So for this coordinate we would place it in quadrant 1 because both numbers are positive. Finally we just line it up with the lines and done. 

How to graph a linear relation

So for graphing linear relations we use the same technique as how to plot a point but we just take it one extra step by connecting all the dots together to make a line.

How to graph vertical and horizontal lines (and determine their equations)

Graphing horizontal and vertical line are simple. You graph them the same as graphing a linear equation it’s just vertical or horizontal. Vertical line follow the Y axes and horizontal lines follow the X axes. Determining their equations is simple because there is only one step. For my example, I am using Y. So, the Y is going straight through the X axes at the 2 spot. So therefor, Y=2. 

Vocabulary  

• X and Y axes: The X axes is the horizontal line on a graph and the Y axes is the vertical line on a graph. 
• T-chart: A t-chart is a type of organizer that organizes variables.
• Coordinate: Two numbers that are placed together on a graph.
• Quadrants (1-4): The 4 quadrants on a graph that determine where coordinates are placed.
• Origin: The center of the graph where both axes are at zero. 
• Plotting: Where you place coordinates on a graph. 
• Linear pattern: Is the line of the point on a graph that are all connected together. 
• Increasing pattern: A pattern that when the Y number increases every time the X gets bigger.
• Decreasing pattern: A pattern that when the Y number decreases every time the X gets bigger. 
• Horizontal line: A straight line going up and down on a graph following the Y axes.
• Vertical line: A straight line going left to right on a graph following the X axes. 

Also include a screenshot of your Initials that you created on Tuesday’s desmos activity

I tried but it was too hard and I couldn’t do it.

Core competency – Self reflection