On Friday we went over the exercises about how to use the intercept and slope-intercepts method. We also were put into groups of 4 or so with white boards to graph the equations that we were given.
Now here is an example of how to use the intercepts method.
(Ahh! If you didn't know what "Intercept" means, here is what I heard from Awot I think to "run into" or to "block".)
That's what the intercepts method means. You look for the two points where the line crosses the X axis and the Y axis. Once you find the line you'll find your coordinates. That's what the intercepts method is about. You look for two points where the line crosses the X-axis and the Y-axis. Once you find those lines you'll find your coordinates.
A question that can be given to you can look like this: "7x + 6y - 42 = 0"
To find the coordinates, you first find the value of X, then the value of Y. Now to find the coordinates you first you want to find the x-axis. How we find the X we solve for X of course. Look at the diagram above, look at the horizantal line that is the x-axis, the X can be anywhere along the line (given the number of course), but the Y will always be a ZERO so don't forget that.
So, to find the X-intercept of 7x + 6y - 42 = 0 (Remember, Y=0)
7x + 6y - 42 = 0
7x + 6(0) - 42 = 0
7x + 0 - 42 = 0
7x - 42 +42 = 0 +42
7x/7 = 42/7
x = 4 --> (4 , 0)
Now that we found our X-intercept, we will want to know the coordinates for our Y-axis. So just like the first one, Y is now a number and X is and always will be ZERO. So now here's how to solve Y.
7x + 6y - 42 = 0
7(0) + 6y - 42 = 0
0 + 6y - 42 = 0
6y - 42 +42 = 0 +42
6y/6 = 42/6
y = 7 --> (0 , 7)
Now here is how it would look like on the grid.
Tada, this is how the two graph looks like with the given coordinates.
The Slope-Intercept Method
Here's something familiar =D This method uses both the "slope method" and the "intercept method" which puts it into ONE equation!
Do you remember what Miss Armstrong told us in class on friday? If not then here's what she said: "By looking at this equation you should know exactly how the graph will looks like."
Now aside from what I just said here is the formula "y = mx + b"
y is the Y-axis
m is the slope
x is the X-axis
and b is the y-intercept
y is the Y-axis
m is the slope
x is the X-axis
and b is the y-intercept
Example of a Graph: 7x + 6y - 42 = 0
Step 1 - Get the equation into y = mx + b form.
7x + 6y - 42 = 0
7x + 6y -6y -42 = 0 -6y
(7x - 42)/-6 = (-6y) /-6
7/6 x + 7 = y
Step 2 - Plot the y int. Step 3 - From b find the second point using the slope. Here's how it would like below.
tada, I hope this all makes sense and quiz on Monday (which is today!) hope you all turned your clocks 1 hour ahead! (please comment!) Hopes this makes sense because I tried hard to understand it this weekend. The next blogger will be.. Arianne!
