i don't understand how to graph an equation. can anyone help me please? i'll greatly appreciate it.
Example: 3x+4y=12
make a table of x and y in columns
to start
x y
0 3
4 0
seeing as how this is a straight line, just put those two points on your graph and draw a straight line through them.
or if you do not believe that, find some more points:
1 9/4
2 3/2
3 3/4
4 0
5 -3/4 etc
thanks a whole bunch. i have just one more question how can you tell whether an equation represents a direct variation?
A direct variation means the graph goes through the origin (0,0) and the output is proportional to a power of the input like
y = x
or
y = x^2
or
y = x^3
or
y = 5 x
or
y = 15 x^2
But NOT
y = x^2 + 3
hey can you also help me out with this problem?
x+2y-4=0
just explain to me step by step so i won't have to bother you anymore. Thanx :P !!!!!!!
That is just the equation of a straight line like the earlier one.
Try x = 0
2 y = 4
y = 2
so (0,2) is on your line
Now try y = 0
x = 4
so (4,0) is on your line.
graph those two points, put a straight line through them.
ohhh i get it. so when you solve for x, you put y as 0. Then when you solve foy y, you put x as 0. am i right?
Of course! I can help you understand how to graph equations. Let's take the example equation you provided, which is 3x + 4y = 12.
To graph an equation, you'll need to follow these steps:
1. Start by isolating one variable in terms of the other. In this case, let's solve the equation for y.
3x + 4y = 12
Subtract 3x from both sides:
4y = -3x + 12
Divide both sides by 4:
y = (-3/4)x + 3
2. Now that you have the equation in the slope-intercept form (y = mx + b), where m is the slope and b is the y-intercept, you can start plotting the graph.
3. Begin by identifying the y-intercept, which is the point where the line crosses the y-axis. In our equation, the y-intercept is 3, so plot the point (0, 3) on your graph.
4. Use the slope (m) to find additional points. The slope -3/4 means that for every 4 units you move to the right, you need to go 3 units down. Starting from the y-intercept, move 4 units to the right, and then 3 units down to find another point. In this case, the coordinates would be (4, 0).
5. Connect the two marked points with a straight line. Keep in mind that a line extends infinitely in both directions, so you only need two points to determine it.
Your graph should now have a straight line that represents the equation 3x + 4y = 12.