SOLUTION: Rewrite the function 2x-3y=-6 as a function of x 3y=2x-6 f(x)=2/3+2 I think this is right. I need to show a graph to show my work. Are the coordinates (3,2), (1,2)? Graphing

Algebra ->  Equations -> SOLUTION: Rewrite the function 2x-3y=-6 as a function of x 3y=2x-6 f(x)=2/3+2 I think this is right. I need to show a graph to show my work. Are the coordinates (3,2), (1,2)? Graphing      Log On


   

Question 127070This question is from textbook Beginning Algebra
: Rewrite the function 2x-3y=-6 as a function of x
3y=2x-6
f(x)=2/3+2
I think this is right. I need to show a graph to show my work. Are the coordinates (3,2), (1,2)? Graphing on Excel is confusing me. This question is from textbook Beginning Algebra

Found 2 solutions by jim_thompson5910, bucky:
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!

2x-3y=-6 Start with the given equation


-3y=-6-2x Subtract 2+x from both sides


-3y=-2x-6 Rearrange the equation


y=%28-2x-6%29%2F%28-3%29 Divide both sides by -3


y=%28-2%2F-3%29x%2B%28-6%29%2F%28-3%29 Break up the fraction


y=%282%2F3%29x%2B2 Reduce


------------------------------------------------------


Now let's graph the equation




Looking at y=%282%2F3%29x%2B2 we can see that the equation is in slope-intercept form y=mx%2Bb where the slope is m=2%2F3 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 2%2F3, this means:

rise%2Frun=2%2F3


which shows us that the rise is 2 and the run is 3. This means that to go from point to point, we can go up 2 and over 3



So starting at , go up 2 units


and to the right 3 units to get to the next point



Now draw a line through these points to graph y=%282%2F3%29x%2B2

So this is the graph of y=%282%2F3%29x%2B2 through the points and

Answer by bucky(2189) About Me  (Show Source):
You can put this solution on YOUR website!
A couple of minor corrections:
.
Your work said:
.
3y=2x-6 <=== this is ok
.
f(x)=2/3+2 <=== a couple of corrections here. The x was left out on the right side and the
constant should have a minus sign. The answer should be:
.
f%28x%29+=+%282%2F3%29x+-+6
.
You can get this into conventional graphing mode by replacing f(x) with y and you have:
.
y+=+%282%2F3%29x+-+6
.
With this equation you can find coordinate points on the graph. For example, let x equal 0. The
corresponding value of y is then determined by substituting 0 for x in the equation for
y. When you do that substitution you find that y = -6. So you then know that the point
(0, -6) is on the graph. Then let x = 3. When you substitute 3 for x in the equation the
right side becomes 2 - 6 = -4. This tells you that the point (3, -4) is on the graph.
And you can continue this process until you get enough points to determine the graph.
.
You should find that the graph looks like this:
.
graph%28600%2C600%2C-20%2C20%2C-20%2C20%2C%282%2F3%29x+-+6%29
.
Hope this helps you to understand the problem and how you can work it.
.