how would you graph this ? im getting confused cause of the fraction

Question

anonymous · Answer

attachment

owlcoffee · Answer

$\frac{ 3 }{ 2 }$ Is just a constant... A number if you prefer.
You see, any Rational or Real number can be represented with the form: $\frac{ p }{ q }$
Where "P" and "q" can represent any natural number you so desire, we can also interpretate it as: " p divided q " which in the very esscence is just a number.
For instance: $\frac{ 1 }{ 2 }$ is exactly the same as "0.5" or $\frac{ 10 }{ 3 }$ is exactly the same as 3.333... .

anonymous · Answer

yeah but how are you suppose to graph that

owlcoffee · Answer

A line, in terms of analytic geometry is the set of all points whose differential quotient (division) gives the same constant "m" which is the "slope" of the line.
The definition is more formal and involves vectors but we can skip that.
So, by the definition I have you, points $a(x_a,y_a)$ and $b(x_b,y_b)$ belong in the same line whose slope is "m" only if: $$\frac{ y_b-y_a }{ x_b-x_a }=m$$
This is the definition of the slope of the line, but what about the equation of the line?...
Let's say point $P(x_p, y_p)$ is a fixed point in the plane and $M(x,y)$ is a variable point we can make to vary as much as we want.
By the very definition of line, this must happen:
$$\frac{ y-y_p }{ x-x_p }=m$$
With some fancy mathematics, we can obtain:
$$y-y_p=m(x-x_p)$$
$$y=mx+(-mx_p+y_p)$$
Thing is that "$-mx_p+y_p$" is just a constant we can name "c", because it's an operation of constants, since "m" represents a constant and so does "xp" and "yp".
So therefore a line can be represented by the equation:
$$y=mx+c$$

owlcoffee · Answer

In order to grap it, you can locate two points but the very equation of the line:
$$y=mx+c$$
Gives away one evident point which is the "y" intersection $\vec y (0,c)$ and all you have to do is assign any value to "x" and then join these two points.

anonymous · Answer

okay yes i know how to do that its just i always have difficulty with the fraction part thats why i posted this how do you graph that onto a graph because i know its not a whole number do you change it into a mixed number and some how convert it or what

owlcoffee · Answer

So, on the line you have to graph: $$y=-\frac{ 3 }{ 2 }x +2$$
The point $a(0,2)$ is a point that belongs to the line, so now, if you were to represent it on the axis, you would just draw a dot on the value "2" on the vertical axis.
If we assign another value for "x", and solve for "y", we cain obtain yet another point, say for instance... $x=1$.
Therefore, instead of writing "x" on the lines equation, we would just plainly write a "1":
$$y=-\frac{ 3 }{ 2 }(1)+2$$
And with further operating:
$$y=-\frac{ 3 }{ 2 }+2$$
$$y=\frac{ -3+4 }{ 2 } \rightarrow y=\frac{ 1 }{ 2 }$$.
So, therefore, the point $b(1, \frac{ 1 }{ 2 })$ belongs to the line as well, and if you represent it, and then join it with the point "a", you'd have obtain the graphic representation of the line.

owlcoffee · Answer

You don't really have to, if you know how to do the basic operations with fractions you should be able to clear them pretty well.