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Chapter 3: Equations and Inequalities in Two Variables; Functions
Transcript of Chapter 3: Equations and Inequalities in Two Variables; Functions
3.2 Slope of a Line
3.3 Graphs and the Equation of a Line
3.4 Linear Inequalities in Two Variables
3.6 Graphing Functions from Equations and Tables
If we were to have a quiz at the beginning of a Ch 1 lecture day, what kinds of things might be on it?
Classify a Given Real Number (1.1)
Match the Statement to its Real Number Property (1.1)
Complete the Exponent Rule (1.4)
Standard Form: Ax + By = C
Vertical and Horiztonal Lines
What kind of line is 4x + 8 = 16?
4x + 8 = 16 can be simplified to x = 2, so it is the vertical line through (2, 0).
Lines with POSITIVE SLOPES go UP and to the right.
Lines with NEGATIVE SLOPES go DOWN and to the right.
The short answer is...
NO!!! The slightly longer answer is...
Division by zero is undefined.
For a more detailed explanation see "Division by Zero" under "Links" on your MyMathLab page.
Anyway...back to slopes of lines.
Sure, so long as x2 - x1 is not zero.
So the slope of a vertical line is undefined and the slope of a horizontal line is zero.
Parallel Lines: Same Slopes
Perpendicular Lines: Slopes are Negitive Reciprocals
Remember the slope m is...
and to find the y-intercept...
3.5 Concept of a Function
Which of these is NOT a function?
A function is kind of like a machine:
You put something in, like a number or variable expression.
The function performs a process on your input. For instance if f(x) = 2x + 5 the process is multply by two then add 5.
Finally you get something out.
If f(x) = 2x + 5 a few examples are:
f(3) = 2(3) + 5 = 11
f(m) = 2m + 5
f(a - 1) = 2(a - 1) + 5 = 2a - 2 + 5 = 2a + 3
Try this out:
After finishing the pattern try to think of a function that would generate that pattern.
If we were to have a quiz at the beginning of a chapter 3 lecture day, what kind of things might be on it?
Equation Forms: Standard and Slope Intercept (3.1, 3.3)
Formulas: Slope and Point-Slope Formula (3.2, 3.3)
Parallel and Perpindicular Lines
Use this POINT-SLOPE formula to find the equation of a line if you know the slope and at least one point on the line.