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What I’ve Learned About Math 9 Linear Relations

What I’ve learned about Math 9 Linear Relations:

 

 

 

 

 

This picture above is an example of a pattern, 1,3,5,7,…

As you notice, the diamond increases by 2 and if there’s a question that asks how many diamonds will be in the 50th picture it will have 99 diamonds.  And how it’s 99 diamonds? Read down below on how I did it.

I learned that Linear Relations is another term for patterns or equation. When making patterns it is important to have a math rule and plot it on a graph.  When making a T-table, there’s the input and output, which merely means X-axis (input) and Y-axis (output).

There are three rules to complete the whole process when doing the patterns:

Example: 4,6,8,…

The first step is to make a T-table.

Those three terms are examples of patterns, and on T-chart it will be placed on the output like the one below.

 

 

 

 

The second step is to make an equation, but you must find the missing x-values first to complete the whole equation.

 

 

 

 

As you can see, the coefficient of x in the equation is 2, and that is because the patterns increase by two which will automatically be 2x.

The third step is to plot it on a graph and use the t chart as a guide to where to plot it.

 

 

 

 

 

 

 

As you can see it is an increasing graph.

I learned that it would be easier to determine which is increasing or decreasing by looking at the lines on the graph. The one above is an example of an increasing chart, and if you see a graph that goes down to the right, it is a decreasing graph. And, the steeper the line is, the closer distance it will have in between the points, and the shallow the line is, the further distance apart the points are.

I also learned about horizontal and vertical lines; To determine which is which, horizontal lines are the ones that go from left to right and across the page, while vertical lines go up and down the page.

As you can see on the graph below, there’s a red and blue line. The blue line is the horizontal line and as you notice it’s across the Y-axis, which tells us that horizontal lines can figure out what is the y-value, but how about x? You can tell that there’s no dot, which means there’s no input (x) The slope of the horizontal line is 0 or undefined. Same goes with vertical lines if there’s no output(y) there will be no slope and will be considered as undefined. For the red vertical line, it’s across the X-axis which means it tells where x is but no slope for this line because the y is undefined.

 

 

 

 

 

 

 

I also learned that if there’s a fraction in an equation, you must be able to find an x-value that can be multiplied and equal to a whole number like this:

 

 

 

Make an empty T-chart for this equation and find a number that will be a good starter like zero:

 

 

 

 

 

After you multiply them both, subtract zero from -1 and the answer will be on the input (y). Then just find numbers that will work and have a whole number, but do make sure that the numbers  have equal distance apart or increase up equally like the one I have down here it goes up by two:

 

 

 

 

 

And these are the things that I have learned from this unit about Linear Relations.

Published inMath 9

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