During this project, I learned about the 3 different equations and converting each of them into each other, I also learned how to  size the lines according to the ones on my initials, you can see the expression I used for domain inside the swirly brackets {} at the end of each of the equations. There was nothing I really found extremely hard during the making of the assignment, but some things I found were annoying in the making of this assignment was converting the equations so that it matched the criteria of all 3 equations displayed at least once per letter. I found this hard because there were sometimes I would make a carless mistake and it would effect the rest of my conversion.

This week, I learned about Slope y intercept, an example is…

first, we got the pair of numbers, then we put it into a T-chart with the left numbers being the input and the right numbers being the output, on the T-chart we see the output numbers are going up by 5 so that’ll be the slope number with x and when we multiply 5 by the input numbers, we still need to subtract it by 2 to equal its output partner, so, -2 would be our y intercept. When we put it into our slope y intercept formula which is y=mx+b which we then get y=5x-2.

This week I learned how to determine steepness of a line, Ex…

before we calculate for the slope, we need to know what the different slopes mean. First we got a positive slope which is on the very right, then we got a negative slope beside it, we then have a normal horizontal line which has a slope of zero always, lastly, we have a normal vertical line which is has an undefined slope.

then we have to know the formula to calculate slope. On this formula, “m” represents slope, and the y numbers as the numerator are the output numbers and the x numbers as the denominator are the input number, and example is…

in this example, we got our 2 coordinates to find the slope of and we first plug the x and y values into our formula, as you can see the yellow underlined numbers are our y values and the green underlined numbers are our x values. Then, we do the subtraction we end up with the slope (m) 1/2 or 2.

This week I learned what functions are. All functions are relations but some relations are not functions, Ex…

A function is a shape on a graph in which the input number (x) has only one partner as the output (y). As you can see, on the example on the right, the numbers on the left circle (input) have only one partner with the right circle (output). On the example on the left, you can see that one of the input numbers (b) is partners with 2 and 3, which doesn’t make it a function. An ex on a number line..

an example of a function on a graph is this example, as you can see no lines overlap each other on the x axis.

this example shows a relation on a graph, as you can see, there are multiple points that overlap each other on the x axis, making this a relation.

One thing I learned this week was set notation and interval notation, some examples are.

when you use set notation with the domain, you use the greater/less then signs to show what space the domain covers on the x axis, in this example, x is less then 4 on the line so you can see that the domain is going to the left and since it does not state where x stops so it goes left forever until it reaches -∞. For interval notations, you first have to put a “D=” which stands for “domain”, when you look at it, it looks like a coordinate on a graph, but the brackets are what tells you everything, when the brackets are rounded it means that it is an open dot which means its not counted when you would do the numbers, if its a closed dot which means it can be applied to the numbers, you use [ ] brackets. Ex.

as you can see in this example, there is an closed dot which means the equation used squared and rounded brackets to express if its an open or closed dot.

One thing I learned this week was relations, the way I solve relations is…

As you can see in the T-chart on the Y side, the numbers are going up by 12, so if we want to find the relation between the X and the Y, then we have to use the clues the t-chart gives us. Aas we have already stated, side Y is increasing by 12 so that gives us the first part of the equation which is 12x=y but if you were to do the math with one of the X values, lets use 1 for this example, 12×1=12 which wont work because the first number of Y is 14, for this we have to modify the equation so it equals 14, for this we add an “+2”. So now the equation becomes 12x+2+y which works because 12×1=12+2=14.

too check if you got the equation right, you can implement the other values of X into your equation to see if it equals the Y value across from it.