Determine if two lines in standard form are (1) parallel, (2) perpendicular, or (3) neither.

System of equations: Determine if two lines in standard form are (1) parallel, (2) perpendicular, or (3) neither. Chapter 0:00 Introduction. 0:16 Parallel lines 1:32 Perpendicular lines 2:55 Neither 3:11 Summary 3:45 Example Note: 1.) Condition for parallel: (I) They have the same slope, and (II) Different y-intercepts. The slope and y-intercept can be found by converting the equation to slope-intercept form (y = mx+b), where m is the slope and b is the y-intercept. 2.) Condition for perpendicular: The slopes are negative reciprocal of each other. 3.) Condition for neither: If the slope are neither equal nor negative reciprocal, the lines are neither parallel nor perpendicular. Example (1) Determine if two lines in standard form are (1) parallel, (2) perpendicular, or (3) neither. Line 1: 2x - 4y = 8 Line 2: −2x + 4y = 12 Step 1: Convert both equations to slope-intercept form (y = mx+b). First equation: 2x − 4y = 8 Subtract 2x from both sides: −4y =−2x+8 Divide both sides by −4 to solve for y: y = (1/2)x−2 So, the slope of the first line, m_1= 1/2 Second equation: −2x+4y = 12 Add 2x to both sides: 4y = 2x+12 Divide both sides by 4 to solve for y: y = 1/2x+3 So, the slope of the second line, m_2 = 1/2. Step 2: Compare the slopes: The slopes of both lines are m_1 = m_2 = 1/2. Step 3: Compare the y-intercepts. The y-intercepts are different, b_1= -2 and b_2 = 3. Conclusions: The tow lines are parallel because they have the same slope but different y-intercepts.