What is a linear relation?

A linear relation is when you have variables that are consistently going up/ changing by the same amount, creating a straight line on a graph. An example of a linear pattern would be: 2, 6, 10… but 3, 5, 11 would not be a linear pattern as the numbers don’t go up by the same amount.

How to find the rule for a pattern: Given the rule (equation), how to know if it is an increasing or decreasing pattern

To find the rule for a linear relation you first make a t-chart, one side titled “x” and the other side titled “y” to organize your numbers. In the “x” column you can write the numbers 1-3 and in the “y” column you fill in the number pattern. Once the chart is filled out you look in the “y” column to figure out what the numbers are increasing or decreasing by. Once you figure out what it is increasing or decreasing by you multiply it by x. If the number from the columns don’t match up you may need to add or subtract.

If you are given a rule to try and figure out if it is an increasing or decreasing pattern you just look at the number in front of x, and if it is a positive number than the pattern is increasing, but if it is a negative number then it will be decreasing.

How to plot a point (coordinate)/ How to graph a linear relation:

When you are given a coordinate to plot on a graph, you are given two numbers that are in brackets. The first on representing x and the second one representing y. To place the coordinate you look for the first number in the brackets on the horizontal line and then find the number on the vertical line so the dot is in like with both of the numbers. To graph a linear relation you do the same thing. To find the coordinates you make a t-chart with the numbers in it and take the x and y values and place them in the brackets.

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

To graph a vertical line, you have to keep the x value the same for every one. If you want to graph a horizontal line you keep the y value the same and only change the x values. It is easy to determine their equations, all you have to do is write x=__ or y=__.

Vocabulary: 

x and y axes – The x and y axes are two lines that are on a graph, x axes is a horizontal line and the y axes is a vertical line.

t-chart – A t-chart is an easy way to organize and help you solve your equations.

coordinate – A coordinate is a set value that shows an exact location on a graph.

quadrants (1-4) – The quadrants are where the coordinates are placed when graphing.

origin – The origin is the middle of the graph, where the x and y axes cross. (0, 0)

plotting – Plotting is when you are placing the coordinates on the graph.

linear pattern – A linear pattern is when the numbers are consistently going up by the same value/ amount.

increasing pattern – An increasing pattern is when the numbers are getting bigger or increasing in value.

decreasing pattern – A decreasing pattern is when the numbers are getting smaller or decreasing in value.

horizontal line – A horizontal line is a line that is going side to side. (East and West)

vertical line – A vertical line is a line that is going up and down. (North and South)

Initials activity: 

 

Core Competencies Reflection: