Linear Equations Review Chapter 5 Chapters 1 2 What you should know about Linear equations Given ANY linear equation you should be able to identify Slope Y intercept X intercept What does the graph look like Parallel slope Perpendicular slope Equation Forms Slope Intercept Standard Horizontal Vertical y mx b Ax By C y b x a Slopes Positive Horizontal Negative Vertical Can you run through the linear equation information 3x 4y 24 y 1 2x 7 y 5 x 6 Given any linear equation one should be able to 3x 4y 24 identify The Equation Form Direction Slope y intercept x intercept Parallel Slope Perpendicular Slope 1 2 3 4 5 6 7 Standard Falling 3 4 6 8 3 4 4 3 Given any linear equation one should be able to y 1 2x 7 identify The Equation Form Direction Slope y intercept x intercept Parallel Slope Perpendicular Slope 1 2 3 4 5 6 7 Slope intercep Rising 1 2 7 7 1 2 14 1 2 2 Given any linear equation one should be able to y 5 identify The Equation Form Direction Slope y intercept x intercept Parallel Slope Perpendicular Slope 1 2 3 4 5 6 7 Horizontal lin horizontal 0 5 Does not exis 0 undefined Given any linear equation one should be able to x 6 identify The Equation Form Direction Slope y intercept x intercept Parallel Slope Perpendicular Slope 1 2 3 4 5 6 7 Vertical line verticle undefined Does not exist 6 undefined 0 To graph a line Intercepts Identify the intercepts Plot the intercepts Draw the line Point slope Identify a point on the line and the slope Plot the point Count the slope Rise Run Graph using intercepts y 3x 7 y int 7 x int 7 3 0 7 3 0 7 Graph using intercepts y 3x 7 point 0 7 slope 3 1 up 3 back 1 0 7 down 3 over 1 The slope formula m y1 y2 x1 x2 This is really the same at the pointslope equation m x1 y1 x2 y1 y2 y2 m x1 x2 Find the slope given 2 points 1 1 2 3 m 3 1 2 1 m 2 3 m 1 3 1 2 m 2 2 3 3 Now write the equation 1 1 2 3 m 3 1 2 1 m 2 3 y 1 y2 m x1 x2 y 3 2 3 x 2 y 2 3 x 4 3 9 3 y 2 3 x 5 3 If you have two points you can find the line sometimes the challenge is knowing what you have Given The origin The y intercept The x intercept A line parallel to the x axis A line parallel to the y axis You have the point 0 0 the point 0 y the point x 0 the slope m 0 eqn is y The slope m undefined eqn is x Parallel Perpendicular II Parallel slopes are equal Perpendicular m original slopes are opposite reciprocals m original m 1 mo m mo Linear equation parts Slope Intercept Standard Horizontal Vertical Equation y mx b Ax By C y b x a Slope m 0 undefined y intercept b b does not exist does not exist a 0 undefined undefined 0 xintercept b parallel slope perpendicul ar slope 1 m m m A C C A B B B A B A Given 3x 4y 12 Find the line to the given line that passes through 2 5 Find the line to the given line that passes through 2 5 Given 3x 4y 12 Find the line to the given line that passes through 2 5 Find the line to the given line that passes through 2 5 If the line is parallel then the slope must be the same so the linear equation will look like 3x 4y If the line is perpendicular then the slope must be the opposite reciprocal so the linear equation will look like 4x 3y Given 3x 4y 12 Find the line to the given line that passes through 2 5 3x 4y 3 2 4 5 6 20 14 Find the line to the given line that passes through 2 5 4x 3y 4 2 3 5 8 15 23 3x 4y 14 4x 3y 23 Given y 2x 12 Find the line to the given line that passes through 2 5 Find the line to the given line that passes through 2 5 Slope m 2 therefore Slope 2 therefore 2 m 1 2 y 2x b y 1 2 x b Given y 2x 12 Find the line to the given line that passes through 2 5 y 2x b 5 2 2 b b 9 y 2x 9 Find the line to the given line that passes through 2 5 y 1 2 x b 5 1 2 2 b b 4 y 1 2 x 4 The alternative calculation is to using the point slope form of a linear equation y y1 m x x1 Once you identify the desired slope you have m then you can substitute the point value for x1 y1 y 3x 7 parallel through 1 2 y 2 3 x 1 perpendicular through 1 2 y 2 1 3 x 1 Find e f remember if you can find the blue line you can find the y intercept then consider the reflection Find t Select t so that the triangle with vertices 4 2 5 1 and t 1 a right triangle with the right angle at t 1 Find t Right angle Select t so that the triangle with vertices 4 2 5 1 and t 1 a right triangle with the right angle at t 1 Switching gears Parametric equations of the line p 69