## week 15 in math 10

this week in math 10 I learned about parallel lines and perpendicular lines. I learned that the slope of parallel lines will always be the same, and that the slope of perpendicular lines will be negative reciprocals. a negative reciprocal for example: if one slope is then the slope of the line perpendicular will be .

I also learned how to convert to point- slope form, to slope- intercept form, to general form, starting with a set of coordinates and a slope.

point- slope : m(x-x2)=y-y2

so if we have a slope of 2/5 and coordinates (5,7) , it would be written out as 2/5(x-5)=y-7

because m= 2/5, x2= 5 and y2= 7

then from there, to convert to slope- intercept form (y=mx+b) we need to isolate y, starting by distributing 2/5 into x and -5, then adding 7 to each side, finishing with +5=y

now to convert to general form (x+y+#=0) we need to get rid of all the fractions, and make sure the leading coefficient of x is positive.

because 2/5x is already positive we just need to move y over by subtracting it from each side, ending up with -y+5=0. then to get rid of the fractions we multiply everything with the common denominator which in this case is 5. general form: 2x-5y+25=0

## week 14 in math 10

this week in math 10 I learned how to identify if a relation is a function. I learned that for a relation to be a function, it basically means that the input must have only have one output. on graph, a function would not have any dots sitting directly above each other:

where as in this graph does not represent a function because there are two points vertically above each other

you can also represent functions through mapping diagrams, a mapping diagram uses arrows to connect the inputs with the outputs, an example of a relation that is not a function would be this because 4, as you can see has arrows to three different outputs.

however this diagram represents a function because it is showing that every input number only has one output/one connecting arrow

## week 13 in math 10

this week in math 10 I learned how to write an equation for y by looking at a set of numbers and using a T chart. for example this set of numbers:

-5,-2,1,4,7,10,13,16

we would draw out a T chart with the left side as X and the right side as Y. x being the input, y being the output. then under the X we would write 1,2,3,4….. and under the Y we would write our -5,-2,1,4,7,10… now we have to find a rule that will get the X number to the Y number, that will also work for all of the numbers. so 1 to -5, 2 to -2, 3 to 1, 4 to 4, 5 to 7 and so on. we can write the pattern of the numbers along with the starting point “start at -5 increase by 3 each time.” because its increasing by 3, we multiple 3 with X and then add/subtract a number to get Y. y=3(x)+or-#

replace x with a number 3(1)= 3 and we have to get to -5 so the equation would be 3(1)-8=-5. we can check if 3(x)-8 works for all the pairs of numbers by replacing X and if it does then the rule for this pattern would be 3(x)-8