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## Welcome to the MM204 Unit 7 Seminar

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**Section 4.1: The Rectangular Coordinate System**Origin Plot: (2, 5) (-3, 4) (1, -6)**Section 4.1**• Standard Form of an Equation • Ax + By = C • If a letter is missing, that means a or b must be zero. Examples: 2x + 3y = -7 3x – 5y = 8 a = 2 a = 3 b = 3 b = -5 c = -7 c = 8**Section 4.1**• A Solution to an Equation • A solution is a point on the line when graphed. • Without graphing, a solution makes the statement true. Example: Is (-1, 1) a solution to 2x – 3y = -5? 2(-1) – 3(1) = -5 Plug in the point. -2 – 3 = -5 Simplify. -5 = -5 True Statement. Yes, (-1, 1) is a solution to the equation 2x – 3y = -5**Section 4.1**• Getting y alone • We need to learn how to get y alone in an equation. This will help us identify the slope. 1: Get rid of fractions. 2: Remove parentheses. 3: Combine like terms. 4: Get all the y’s on one side and everything else on the other side. 5: If there’s a number in front of y, divide both sides by it. 6: Simplify if necessary.**Getting Y Alone**Example: Solve 3x + 5y = 15 3x - 3x + 5y = -3x + 15 Subtract 3x from each side to get the y-term alone. 5y = -3x + 15 Simplify on each side. Divide by 5 on both sides. Simplify.**Getting Y Alone**Solve 4x + 2(5 - y) = 6 for y. 4x + 10 - 2y = 6 Use the dist. prop. to get rid of parenths. 4x + 10 - 10 - 2y = 6 - 10 Subtract 10 from each side to get y-term alone. 4x - 2y = -4 4x - 4x - 2y = -4x - 4 Subtract 4x from each side to get y-term alone. -2y = -4x – 4 Divide each side by -2 to get y alone. y = 2x + 2**Section 4.1**• Finding Missing Coordinates • Given an x or y. • Plug into equation to find missing coordinate. Example: Find the missing coordinate: 2x + 3y = 5 and (2, ?) 2(2) + 3y = 5 Plug in 2 for x. 4 + 3y = 5 Simplify. 3y = 1 Subtract 4 from each side to get y-term alone. y = 1/3 Divide both sides by 3 to get y alone. The point is (2, 1/3).**Section 4.2: Graphing a Linear Equation**• Steps for Graphing a Linear Equation 1. Determine three ordered pairs that are solutions to the equation. 2. Plot the points. 3. Draw a straight line through the points. Example: Let’s graph the equation 2x + y = 6 To determine three points, we get to pick numbers for x and/or y! We’ll do that on the next slide.**Finding Points**Graph 2x + y = 6. x 2x + y = 6 y (x, y)**Graphing**Plot the points: (0, 6) (3, 0) (1, 4)**Memory Aids for Lines**• HOY • Horizontal lines. • 0: Zero (0) slope. • Y = number will be what the equation looks like. • VUX • Vertical lines. • Undefined slope. • X = number is what the equation will look like.**Section 4.3: The Slope of a Line**• Slope • Tells us how the line will slant on the graph. • Formula: m = Example: Find the slope of a line that passes through the points (2, 3) and (5, 7). m = m =**Section 4.3**• Slope – Intercept Form • y = mx + b • m is slope. • (0, b) is the y-intercept. Example: What is the slope and y-intercept for y = -5x + 7? Slope is -5. (0, 7) is the y-intercept.**Section 4.3**• Parallel Lines • Same Slope! Example: Line A has a slope of 5. What is the slope of every line parallel to Line A? Since parallel lines have the same slope, the slope must be 5.**Section 4.3**• Perpendicular Lines • Opposite, Reciprocal Slopes Example: Line A has a slope of 5. What is the slope of every line perpendicular to Line A? Since perpendicular lines have opposite, reciprocal slopes, the slope must be .**Thanks for Participating!**• AIM: tamitacker • Read, read, read! • Email me if you have questions.