ok i think graphing would be the easiest way to do this :D do u have geogebra app?
yeah im here
and no i dont have a graphing app
hmm is it fine if i graph it and u determine how many solutions the line will have? solution is just the intersection so it's easy :)
ok sounds good :)
great! :D so first are u familliar with the slope-intercept formula?
y= mx + b ?
sorry my mom was talking to me
but yes i am familiar with y=mx+b
it's cool :) so i guess you know that m stands for slope and b represents the y-intercept
awesome! so if two lines have the same slope, it means thy are parallel. And if two lines are parallel, they will NEVER intersect which means there will be no solution so do u see any lines with the same slope?
oh ok that makes sense and idk i dont know how to graph them
no we dont need to graph it if we find any two equations that have the same slope for example y= 3x +1 and y= 3x +2 have the same slope,3 so the lines are parallel so there is no solution ( they will never intersect) make sense?
what about the last on is that no solution?
so if u look at the first pair, you can tell that they have the same slope because -x is the same thing as -1x
and the second last one is no solution
hold on we're on the first one
y= -x -2 y= -x -6 do this equations have the same slope? ^^
um actually they do, look -x means -1x so we will have y= -1x -2 y= -1x -6 they both have a slope of -1
ohhh... i thought they didnt because of the 2 and the 6
that's the y-intercept , the slope is the one with x :)
i dont get these they are very confusing sooo the numbers dont count ?
sorry about the confusion :/ butt here y=mx+b we will be given numbers for m and b like y= 2x + 3 m = slope b= y-intercept so in this case our slope is 2 and the y-intercept is 3 got it?
idk i just suck at everything that has to do with graphs and slopes :/
no it's okay just remember m represents slope and b represents y-intercept okay
but youre explaining everything very well :)
thanks for not leaving :)
my pleasure dear (:
ok so can u remember that m means slope and b means y-intercept ?please :DD sorry if i sound rude
yes ma'am i remember
im just confused about how do you know if its one solution or infinity
we'll get there but for now you have to know how to determine the slope and y-intercept |dw:1433842646745:dw|
so if m is slope then whats the slope in the above equation?
YES!! :DDDD *high fives* great job! :D what about the y-intercept?
3... i understand all of that
oh okay so now do u understand why i said the first two pairs have the same slope?
the y=-x-2 ?
awesome so since they are parallel they will be included in the "no solution" section :) got it?
yeahh is the next one 1 solution ?
YES! awesome job! :D
is the rest 1 solution?
no the third one is different and maybe the rest as well for the 3rd one we have y=3x+4 and 2y=6x+8 lets change 2y= 6x+8 in to y=mx+b form by dividing 2 from both sides 2y/2 = 6x/2 + 8/2 y= 3x+4 now we have the SAME equation! :O this means the lines have infinitely many solutions
was that confusing?
not the way you explained it but if i were to do it by myself id be lost
im glad :D let's move to the fourth one we have y=-3 and x= -6 one sec, i'll post the screenshot of what the graph will look like
http://prntscr.com/7f1e2v so how many intersections do u see? :P
i mean where the blue and red line intersects
is that 1 solution?
yes, you're doing great! :DD take a look at the last one http://prntscr.com/7f21uy
YAYY! WE'RE DONE AND AWESOME JOB!! :DDD
Thank youu so muccchhhhhhhhh
you're very welcome (:
have a nice dayyyy