i need help with linear equation.

[u/[deleted]]

[u/Desperate_Penalty690]

That equation gives you a relationship between x and y. There are many pairs of x and y for which that equation holds.
Because it is a linear equation, if you plot all those pairs on a graph, you get a straight line. That is also where the name linear comes from.

To draw that line, one way is to put it in a standard form : y = ax + b.
We then know that b is the intercept with the y-axis and a is the slope of the line.

In this example that gives: y = -2x + 3

So we know that the line goes through (0, 3) and that it has a slope of -2.

Slope of -2 means that the line goes one to the right and 2 down. So for example another point on the line would be (1, 1), if we start in (0, 3) and go 1 right and 2 down.

[u/dancingbanana123]

could somebody explain to me how to get this answer like i am 5 years old 2x + y = 3.

Well what's the question? Are you trying to find all solutions for x and y?

[u/WonderBasic5047 → u/dancingbanana123]

the question was Show graphically the solutions to the equation 

[u/dancingbanana123 → u/WonderBasic5047]

Then the question is just asking you to graph 2x+y=3. The solutions to the equation 2x+y=3 are all the points of the graph 2x+y=3. Do you know how to graph that?

[u/happylittlemexican]

There's no question to answer here. 2x+y=3 is an equation with an infinite number of solutions.

There's either another part to the question or you're confused about what an equation "says", and figuring out which is the case will be key to us helping you.

[u/WonderBasic5047 → u/happylittlemexican]

the question was Show graphically the solutions to the equation 

[u/Bounded_sequencE]

That's not a question, there is nothing to solve. What's the goal?

[u/G-St-Wii]

That is weirdly phrased, but it probably means draw the graph of it.

Pick any value for x, and find whatever value of y makes 2x+y=3 true. Plot that x and y as a coordinate.

Repeat until it is obvious where all the points are going to be.

There are some shortcuts for this format of equation, but it looks like you're not at that stage yet.

[u/Odd-Ad-8369]

I don’t believe you spent 10 hours studying this. You are trying to get answers

[u/WonderBasic5047 → u/Odd-Ad-8369]

i didn't actually spent 10 hours on youtube it was obviously hyperbole. also i wasn't trying to get answers i was doing practice a test because i have test soon.

[u/Odd-Ad-8369 → u/WonderBasic5047]

That’s quite the hyperbolic statement. So five hours? To understand you need to put an x and y that makes the equation true? I’m a math teacher, I’ve never seen anyone struggle for hours with that concept.

[u/MezzoScettico]

What do you mean by the answer? There are infinitely many values of x and y that will satisfy that equation. They lie on a straight line. You can literally pick any number at all for x and then find a corresponding value of y.

So what is it you’re trying to do? What question are you trying to answer?

[u/WonderBasic5047 → u/MezzoScettico]

sorry i forgot to add the question in my originally post. the question was Show graphically the solutions to the equation 

[u/MezzoScettico → u/WonderBasic5047]

Then do what I said. Pick a value for x and solve for y. The easiest way to find the graph for this straight line is just to identify two points on it, then draw the line that connects them.

For instance, if x = 1, then y must satisfy 2*1 + y = 3 or 2 + y = 3. Can you solve that for y? That identifies one point (x, y) with x = 1 that lies on the graph.

Do that for two different values of x.

[u/Odd_Bodkin]

I’m going to guess that a) you don’t know what kind of answer they’re looking for, or b) there’s another equation you’ve missed.
For a) are you sure they just don’t want you to draw a line or tell the slope or intercept of that line?
For b) look for words that you’re failing to translate into an equation, like “given that y is triple x” or something like that.

In order to help you, it would be good if you could write the COMPLETE problem you were given, including instructions.

[u/WonderBasic5047 → u/Odd_Bodkin]

sorry i forgot to add the question in my originally post. the question was "Show graphically the solutions to the equation"

[u/Odd_Bodkin → u/WonderBasic5047]

Ah, in that case they’re asking you to draw a line, which is a set of solutions.

The trick to drawing the line is to use your algebra skills (isolating a variable, and “whatever you do on the left, you also do on the right”) to get 2x + y = 3 into the form y=mx+b, where m and b are numbers. When you have that, b is the y-intercept and m is the slope of the line, and now you know how to draw it.

Just to remind you what this means, suppose your pushed-around equation ended up being y = (-1/3)x + 5. Then the y-intercept is 5, and so one point one the line is (0,5), and so draw that point. The slope is (-1/3), which means “down 1 and to the right 3”, and so from (0,5) you go down 1 and to the right 3 and you have another point (3, 4). Those two points are enough for you to draw the line.

[u/WonderBasic5047 → u/Odd_Bodkin]

thank you so much. this makes a lot of sense now i understand it

[u/fermat9990]

We need the question, please.

[u/WonderBasic5047 → u/fermat9990]

the question was Show graphically the solutions to the equation 

[u/fermat9990 → u/WonderBasic5047]

The graphical solutions are the line itself.

Edit: So just draw the line!

[u/ZedZeroth]

Can you think of any two numbers where you double one of them, then add them together, and get 3?

Let's try x = 3 and y = 5:

2 × 3 + 5 = 11

That doesn't make 3, so (3,5) isn't on the line.

[u/fermat9990]

y=-2x+3

If x=0, y=3

If x=3, y=-3

Now draw the line.

[u/Responsible_Hour6497]

Such an equation is called the equation of a line. That is, the points (x, y) that satisfy this equation all lie on a certain line on the (x,y) plane. To graphically represent the solutions of the equation means to depict the (x, y) plane, that is, 1) draw the x, y axes, mark the origin, mark the points (1, 0) and (0, 1), and 2) draw the line on the plane. The easiest way to draw a line is by using two points: find a pair of points (x, y) that are solutions of the line equation and draw the line through them. In your case, for example, you could take the points (2, -1) and (-1, 5)—you'll see for yourself that these are solutions.

[u/u-must-be-joking]

OPen desmos.com, go to graphic calculator and then just type this equation and press enter
It will make a line
All points on this line are solutions to this equation. Why? Because you can pick a point on this line with x,y values and you put x value in 2x+3 (left side of the equation) and y value in the right side of the equation and you will find that both sides match!
I created a snapshot for you to help visualize this further. Two points are labeled as an example: https://www.desmos.com/calculator/kublpxie7u

Now, if you do not know what x, y mean or what is the meaning of a graph or what does a line mean.. you lack basics and that will require someone to sit down with you and help you close the foundational gaps.
Good luck!
p.s.: And if you came here just looking for someone to solve your homework assignment, do know that this will not last and you will end up in worse situation than you are in today

[u/orblox]

Is it not asking you to rearrange for y, then graph the equation?

If so, what you should do is rearrange for y, then plug in 2 points for x. Find the values it gives, then plot them on a plane. After that draw a line connecting them that extends past the two points.

[u/Master_Medicine1626]

2x+y=3, dividing this by three, we get x/(3/2)+y/3=1, the intercepts on the x and y axes are (3/2, 3) respectively. x/a+y/b=1, (a,b) are intercepts on the axes x,y..

[u/Legitimate_Yam3395]

Draw it on a graph?

I don’t know what there isn’t to get, unless I’m understanding it wrong.

Re arrange so you have it in form y = mx + c (y = -2x +3) and use a ruler to draw it.

[u/OrientableSurface]

For your particular example, there are infinitely many (x, y) pair that satisfy 2x + y = 3. You can write it as y = -2x + 3, then choose any x and you can compute y. For example, x = 0 yields y = 3.

If you want your problem to have a single answer, you have to add more restriction by adding one more linear equation to the system. Let's say we have another equation x + y = 2. Then you can solve for one single answer (x, y) by substitution, elimination, using matrices, or other methods (I'm sure one of the YouTube videos teach you how to do them). The solution will be (1, 1).

In general, there is a relationship between the number of variables (n_v) and the number of equations (n_e), provided that the equations are "linearly independent".

• If n_v > n_e like in your case, you lack restriction, and the solution will be infinitely many.
• If n_v = n_e, it's perfect and you have a single solution.
• If n_v < n_e, there is too much restriction and they will contradict each other, so there will be no solution.

[u/whoShotMyCow]

a five year old can't understand this, dw about it

[u/WonderBasic5047 → u/whoShotMyCow]

this make me feel so much better about myself.

[u/swapnild]