x+2y=6
2x+4y=32
how would i graph them and what would be my points?
easy way to graph a straight line is to use the intercepts
for the first one:
let x=0, y = 3, (should be able to do this in your head)
let y = 0, x = 6
so you have two points, (0,3) and (6,0)
plot the points and join with a straight line
Do the same with the 2nd equation
it should look like this:
http://www.wolframalpha.com/input/?i=plot+y+%3D+-2x%2B6%2C+y%3D%2832-2x%29%2F4
To graph these equations, we first need to rearrange them in the form y = mx + b, where m represents the slope and b represents the y-intercept.
Let's start with the first equation:
x + 2y = 6
First, isolate y by subtracting x from both sides:
2y = -x + 6
Then divide the entire equation by 2:
y = -0.5x + 3
Now we have an equation in slope-intercept form: y = mx + b, where m = -0.5, and b = 3.
To graph this equation, start by plotting the y-intercept, which is the point (0, 3). From there, use the slope (rise over run) of -0.5 to find additional points. In this case, for every 1 unit we move to the right (run), we must move 0.5 units down (rise).
For example, from the y-intercept (0, 3), move 1 unit to the right and 0.5 units down, to the point (1, 2.5). Repeat this for a few more points, such as (2, 2), (3, 1.5), and so on.
Now let's move on to the second equation:
2x + 4y = 32
Isolating y, we have:
4y = -2x + 32
Divide the entire equation by 4:
y = -0.5x + 8
Again, we have an equation in slope-intercept form: y = mx + b, where m = -0.5, and b = 8.
Following the same procedure, plot the y-intercept (0, 8) and find additional points using the slope of -0.5: (1, 7.5), (2, 7), (3, 6.5), and so on.
After plotting the points for both equations, you will notice that they intersect at a single point. This point represents the solution to both equations.