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 3/4 x then the slope of the line perpendicular will be -4/3x .

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 2/5 x +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 2/5 x -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