how do you graph this? im so confuuuused!?

Question

i aleady solved the equations but i dont know how to plot it on the graph. like which direction do i draw the lines after i plotted the points? do i need a graphing calculator? i lost mine, but how would you do it on a graphing calculator?

the equations are 3x + y = 5 & -2x +3y = 4
i looked up on a site that you have to split the equation into two halves and write down two equations each starting with 'y =' followed by half of the original equation. im confused!

Answer 1

first solve for y

You should have something like

y = -3x + 5, and y = 2/3 x + 4/3

Now, the formula for a straight line is

y = mx + b

m is the slope

b is the y-intercept:: (0,y)
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to graph. All you do is look at b.

A positive number will move you up, and a negative will move you down.

So, if b = 5 just like in your problem. 5 is positive so you move up 5 from the origin. The origin is the point (0,0) in the center where the x-axis and the y-zxis cross.

Now that you are up 5 lines/ units, DRAW A DOT at that point. (0,5)

(0,5) just means that you have no movement left or right, since x = 0, and you have to move up 5 on the y-axis, b/c y is positive 5.

Next, you use the slope. Here it is -3x.
Again, the formula is y = mx + b, we know what to do with be.

m = -3, or -3/1. So, we go down 3 lines or units, and right 1.

You can now DRAW A DOT at the (1,2) b/c that is where you should end up.

TRY IT.

Now you can DRAW A LINE THOUGH the dots to make your graph. Do the same with the other problem, but remember that fractions are not whole numbers. 4/3 =1+1/3
you can use the slope to make your first point.

Answer 2

Solve the equations for y: you obtain y=5-3x and y=(4/3)+(2/3)x. You can use the value for x=0 and x=1 to draw a segment and find the corresponding line.

More in detail: let's find how to draw y=5-3x. Plug in the value 0 and you obtain 5. Plug in 1 and you obtain 2. So the segment you want to draw has ending points (0, 5) and (1, 2). Once you have drawn the segment, it's easy to draw the line that contains it.


You don't need a graphing calculator (these functions are extremely easy to sketch). However, if you want to plot the graph, I suggest you use Gnuplot. It's for free and quite simple to use (for most basic tasks): to plot the graph just type:

plot 5-3*x, (4/3)+(2/3)*x


I hope it's clear and helps.

Answer 3

The easiest way to do it is by using basic algebra and solving for Y.

on the first equation: y=5-3x
on the 2nd equation: y=(4+2x)/3

So plug in '1' for 'x' on both equations. You then get '2' for equation one, and '2' for equation 2.

When x=2, y= -1 for equation 1 and 8/3 for equation 2.

So now you have for equation 1:
(1,2) and (2,-1)

For equation 2:
(1,2) and (2,8/3)

Just keep multiplying it out, and then plot the points and connect the dots. Good luck!

Answer 4

A look at the eqns, and you should recognise them as straight lines as they are both linear eqns.

In order to plot straight lines, you just need 2 pts. And the easiest way to start is to find the y-intercept (found by letting x=0 for each eqn) of the graphs and x-intercept (found by letting y=0 for each eqn) of the graphs. After marking out these 2 pts (for each eqn), you can then join them up to find the graph of the line.

Answer 5

Take each equation and solve for its INTERCEPTS,.. plot them, then DRAW A LINE through them.

Taking the first one:

X INTERCEPT, (Y=0)
3x + 0 = 5
x=5/3

Y INTERCEPT, (X=0)
3(0) + y = 5
y = 5

PLOT POINTS, (intercepts):
One point on x axis at 5/3
One point on y axis at 5

Use a straight edge to draw a line through these.
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Follow the same steps for the second equation.