Good to the Last Drop!

Inequalities have come back from the dead! Just when we thought we left those suckers in our dust back in Unit 2, they have come back. However, this time we know what to do with them, so their “vengeance” isn’t so grand after all. There’s a little table that you should remember in addition to the normal inequality “FLIP!” rules:

.                Shade Above           Shade Below
Solid                ≥                                 ≤
Dash                >                                 <

Using the table above, graphing linear inequalities should be like a walk in the park on a warm, sunny day.

Notes: Lesson 25 Linear Inequalities
Assignment: (A25) linear inequalities

P.S. Don’t forget, tomorrow is EARLY RELEASE!

A Full Moon on Monday

It may have been Monday and it may have been a Full Moon, but we just have to keep on keeping on in Math class. There’s a saying that goes “No sleep for the weary.” Well, that is how this class is – No time to play around and have a free day…or is there?

Today wasn’t too bad in the sense that we were just writing the equations of lines, after we found the key pieces of course. We know that you need the slope and y-intercept for slope-intercept form. But, what about point-slope form? Well, in that case, you need the slope and any point on the line. No matter which form you use, you should still get the same equation in the end!

Notes: Lesson 24 Writing Equations
Assignment: (A24) writing equations of lines

6 Weeks Down!

Can you believe it’s already been 6 weeks since the start of school? This also means that we are 1/3 of the way through with this semester…and Math Models course for that matter!

Today, we talked about the X- and Y-intercepts of a graph and how if you can find both of them, you can graph a line. This is because they give you two points on that line, assuming we aren’t taking a trip through the origin. We learned how to identify the intercepts from graphs, tables, and even equations. On Monday, we’ll talk even more about lines, so stay tuned!

In the meantime, it may be wise to complete any assignments that have not been turned in, as Progress Reports come out Thursday!

Notes: Lesson 23 X- & Y-Intercepts
Assignment: (A23) x and y intercepts

Broken Record

If by now I sound like a broken record, then chances are pretty high that you have been paying attention this semester. Today was the third day that we mostly just graphed equations. If you take into account having to read graphs, I bet we are pushing close to 6 or 7 days. That means that today was all about y = mx + b, where “m” is the slope and “b” is the y-intercept. There’s not much to say here because it’s that simple – you plot the intercept and then move according to how the slope tells you to move.

Notes: Lesson 22 y=mx+b
Assignment: (A22) y = mx + b

Change is the Only Constant

That’s one thing that we all probably learn throughout life: No matter how much we try to keep things the same, they always seems to change. With that being said, change isn’t always a bad thing. Take today for instance, we learned about Rates of Change, which are real-world applications of Slope. Think about if you had a car rental company, would it be fair to charge someone who drove 100 miles the same as someone who drove 1,000 miles? Probably not. While we may not stop and draw a graph for comparing multiple companies, we are stilling using the same concepts to see which company is the better option.

Notes: Lesson 21 Rate of Change
Assignment: (A21) Rate of change

Slippery Slopes

What a slippery two days these will be! We will be sliding all over the slopes as we find just that…the slope! Today, we saw the formula and graphing side of slope. For the graphs, we simply would just count the spaces using “rise over run”. When given two points, we have a handy-dandy formula that we can use that’s m = (Y2-Y1) / (X2-X1). Tomorrow, we will look at slope as it relates to real-world situations. Stay Tuned…

Notes: Lesson 20 Slope
Assignment: (L20) Slope

They’re Everywhere! They’re Everywhere!

That’s what it seemed like we were saying today as we did nothing but graphing once again. This time, though, they equations weren’t already in slope-intercept form and so we had to convert them into that form. That’s okay, though, because as long as we can solve for y, we have it licked! This is just the start of this unit, though, as we will see this concept come up time and time again until we feel like experts for the next two weeks.

Notes: Lesson 19 Graphing
Assignment: (L19) Graphing

Real-World Problems, Real-World Answers

A lot of what we saw today were practical examples using slope-intercept form to model the equations. While you may not sit down and do the Algebra with graphs, equations, etc., it is going on behind the scenes when you are thinking about money, plane altitude, construction service calls, etc. This is the precise reason why knowing how to use slope-intercept form is so important and why we will keep hitting on it time and time again until the cows come home. Anyways, if you need the notes, they are below. One note: The page that says “Lesson” is your assignment and the pages that say “Assignment” are your notes.

OH! One more thing, we will have a test this Friday. Make sure you start studying NOW!

Notes: Lesson 17 y=mx+b Word Problems
Assignment: (L17) Slope-Intercept Form Word Problems