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

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

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

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

So the equation is now in slope-intercept form () where the slope is and the y-intercept is

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

So the equation changes to the function

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is

Since 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

Also, because the slope is , this means:

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

So this is the graph of through the points

and

# 2

Start with the given equation

Subtract from both sides

Rearrange the equation

Divide both sides by

Break up the fraction

Reduce

So the equation is now in slope-intercept form () where the slope is and the y-intercept is

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

So the equation changes to the function

Looking at we can see that the equation is in slope-intercept form where the slope is and the y-intercept is

Since 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

Also, because the slope is , this means:

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

So this is the graph of through the points

and

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