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DA Algebra 1-1 4.4 Notes 2016 X & Y Intercept and Parallel & Perpendicular Lines Notes Objective: You will be able to graph a linear equation from SIF, PSF, and Standard Form using x and y-intercepts. You will understand parallel and perpendicular lines. The graph of the linear equation 2x + 3y = 6 is displayed below. Write the ordered pairs representing the x and y intercepts on the graph. The x-intercept is the value of x when y = 0. x-intercept ___________ The y-intercept is the value of y when x = 0 y-intercept _______________ Confirming/Finding x and y intercept algebraically. To find the x-intercept: To find the y-intercept: Write the original equation: Write the original equation: Substitute 0 for y: Substitute 0 for x: Solve for y: Solve for x: The x-intercept is ___________ The y-intercept is ___________ The line crosses the x-axis at the point ______ The line crosses the y-axis at the point ______ Graph the equation -3x + 6y = 18 by making a quick graph using the x and y intercepts. Step 1: Find the x-intercept: Step 2: Find the y-intercept To find the x-intercept: To find the y-intercept: Write the original equation: Write the original equation: Substitute 0 for y: Substitute 0 for x: Solve for x: Solve for y: The y-intercept is _________ The x-intercept is _________ The line crosses the y-axis at the point ______ The line crosses the x-axis at the point ______ Step 3: Plot and label the x-intercept and the y-intercept Step 4: Draw a line connecting the x and the y intercepts. Step 5: Label the line. Practice: Graph using x and y intercepts. 5 x 3 y 15 Practice: Find the x and y-intercept of the line. Graph the equation. 1.) y = -6 + 3x 2.) -x + y = -3 3.) 4x + 5y = 20 4.) -y = -2x – 4 Part 2: Algebraically Practice Finding the X and Y Intercept Algebraically Find the x and y-intercepts. Remember: For the x-intercept, find the value of x, therefore substitute 0 for y and solve. For the y-intercept, find the value of y, therefore substitute 0 for x and solve. a. 2x + y = 6 b. 4x + 8y = -32 c. y = x + 5 x-intercept: ________ x-intercept: ________ x-intercept: ________ y-intercept: ________ y-intercept: ________ y-intercept: ________ Practice d. y = -8 – 2x e. -4x + 16y = -16 x-intercept: ________ x-intercept: ________ x-intercept: ________ y-intercept: ________ y-intercept: ________ y-intercept: ________ f. y = 1 x + 10 2 PART 3: X & Y-Intercept application 1. To raise money for a charity, your club is selling flowers and candy on Valentine’s day. Each rose cost $2.50 and a box of candy cost $10. Your club made a total of $340 for charity. a) Write an equation in Standard Form (Ax + By = C) representing this situation. Let x be the number of flowers and y be the number of candy boxes. b) Identify and interpret the x-intercept. c) Identify and interpret the y-intercept. 2. The graph below shows the relationship between the number of days and the pages left to write an English paper. a) Identify and interpret the slope b) Identify and interpret the x-intercept c) Identify and interpret the y-intercept PART 4: Parallel and Perpendicular Lines Example 1: Parallel and Perpendicular Lines A. Find the slope of lines a and b. B Find the slope of lines c and d. Line a: ______ Line b: ______ Line c: _________ Line d: ________ Lines are parallel if Lines are perpendicular if Partner Practice: Identifying/graphing parallel and perpendicular lines. Rewrite each equation in SIF and graph. Label your lines. A. –x + 2y = 6 B. –x + 2y = -2 C. 2x + y = 4 Example 2: 1) For lines to be parallel, what must be true about their slopes?_________________________ 2) Give an example of two slopes that are parallel. _________________ 3) For lines to be perpendicular, what must be true about their slopes?__________________________ 4) Give an example of two slopes that are perpendicular. __________________ 5) What form must an equation be in for you to know the slope? _________________________ 6) What is always true about the slopes of horizontal (y = #) and vertical (x = #) lines? _______________________________________________________________________ 7) Write the equation of a line that is perpendicular to y = 2 _______________ (hint: it may help if you graph the line) Practice 1) Are these lines parallel, perpendicular, or neither? (Get equations in slope intercept form first. Then circle the slopes). Justify your answer. a) y = -6x +2 b) y = 9x – 3 c) y = 2x + 3 y = -6x -1/9 x + 2 = y y = 7 – 2x