SOLUTION: how to write 12x + 3y = 6 in function form and then graph. also 4x - 2y = 16

Algebra ->  Equations -> SOLUTION: how to write 12x + 3y = 6 in function form and then graph. also 4x - 2y = 16      Log On


   

Question 128458: how to write 12x + 3y = 6 in function form and then graph.
also 4x - 2y = 16
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
# 1


12x%2B3y=6 Start with the given equation


3y=6-12x Subtract 12+x from both sides


3y=-12x%2B6 Rearrange the equation


y=%28-12x%2B6%29%2F%283%29 Divide both sides by 3


y=%28-12%2F3%29x%2B%286%29%2F%283%29 Break up the fraction


y=-4x%2B2 Reduce



So the equation is now in slope-intercept form (y=mx%2Bb) where the slope is m=-4 and the y-intercept is b=2


So to get the equation into function form, simply replace y with f(x)



So the equation changes to the function f%28x%29=-4x%2B2






Looking at y=-4x%2B2 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=-4 and the y-intercept is b=2


Since b=2 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is -4, this means:

rise%2Frun=-4%2F1


which shows us that the rise is -4 and the run is 1. This means that to go from point to point, we can go down 4 and over 1



So starting at , go down 4 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=-4x%2B2

So this is the graph of y=-4x%2B2 through the points and






# 2





4x-2y=16 Start with the given equation


-2y=16-4x Subtract 4+x from both sides


-2y=-4x%2B16 Rearrange the equation


y=%28-4x%2B16%29%2F%28-2%29 Divide both sides by -2


y=%28-4%2F-2%29x%2B%2816%29%2F%28-2%29 Break up the fraction


y=2x-8 Reduce



So the equation is now in slope-intercept form (y=mx%2Bb) where the slope is m=2 and the y-intercept is b=-8



So to get the equation into function form, simply replace y with f(x)



So the equation changes to the function f%28x%29=2x-8





Looking at y=2x-8 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=2 and the y-intercept is b=-8


Since b=-8 this tells us that the y-intercept is .Remember the y-intercept is the point where the graph intersects with the y-axis

So we have one point




Now since the slope is comprised of the "rise" over the "run" this means
slope=rise%2Frun

Also, because the slope is 2, this means:

rise%2Frun=2%2F1


which shows us that the rise is 2 and the run is 1. This means that to go from point to point, we can go up 2 and over 1



So starting at , go up 2 units


and to the right 1 unit to get to the next point



Now draw a line through these points to graph y=2x-8

So this is the graph of y=2x-8 through the points and