Chapter 3.3 – 3.5 Linear Equations and slope Alg. 2 Notes Name:__________________ Date:________________

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

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

Example : Graph 3x – 4y = 12

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)

Example : Graph y = 3x – 2

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!!!!

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!!!!

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

Slope from a graph: