1. Chapter 3.3 – 3.5 Linear Equations and slope
Alg. 2 Notes
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2. Example 1: Which are linear? A. 3x2 + 2y = 7 B. 5x = 1 C. 3xy = 1
Linear Equations
No product of variables
No variables in denominator
1st degree only
Example 1: Which are linear?
A. 3x2 + 2y = 7
B. 5x = 1
C. 3xy = 1
D. y = 3x + 1
E. y = 1/x

3. Graphing Linear Equations Method 1: Standard Form: COVER-UP METHOD
Ax + By = C
► Find x – intercept: cover up y-term and
solve for x
► Find y – intercept: cover up x-term and solve for y
► Slope is

4. Example : Graph 3x – 4y = 12

5. Method 2: Slope intercept form
y = mx + b
► start at “b” on the y-axis
► use slope, “m”: move up or down then over (right)

6. Example : Graph y = 3x – 2

7. Horizontal & Vertical Lines Vertical lines “hit” x-axis → x = #
We are saying what x or y is while the other takes on all real numbers.
Horizontal & Vertical Lines
Vertical lines “hit” x-axis → x = #
Horizontal lines “hit” y-axis → y = #
Example : Graph x = 4
No y so…
can’t cross y (parallel to y-axis)
Possible Solutions:
( , -2) ( ,0) ( ,3)
Slope =
(Rise ÷ 0 (no run) is error)
Makes :
Notice x stays 4!!!!

8. Example : Graph y = -2 No x so can’t cross x (parallel to x-axis)
Possible Solutions:
( -1 , ) ( 0 , ) ( 1, )
Slope =
(No Rise)÷run
Makes:
Notice y stays -2!!!!

9. Steepness from one point to another
Slope:
Steepness from one point to another
Ratio of vertical change, Δy, to horizontal change, Δx.
Written as:
Find the slope:
Example 1: (3, 5) and (-2, 8)
Example 2: (-5, 4) and (-1, -9)
Doesn’t matter which points is called y2 or y1 as long as ordered pairs stay together

10. Slope from a graph: