Warm Up 1. Find the function for the line parallel to y = 3x – 7 but which crosses the y-axis at y = 3. 2. Find the function for the line perpendicular.

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Warm Up 1. Find the function for the line parallel to y = 3x – 7 but which crosses the y-axis at y = Find the function for the line perpendicular to y = 3x – 7.

Given a line (either as a function or as a graph in the coordinate plane) how can we determine the function of a line parallel or perpendicular to that line? Parallel and Perpendicular Lines

Bobby leaves his house at 10 am heading due east. The distance he has traveled d = 55t, where d is in miles and t is the time in hours, with t = 0 being 10 am. Travelling on the same road and at the same speed and in the same direction is Bobby's friend Johnny. Johnny left earlier than Bobby, and at 11am Johnny is already 300 miles past Bobby's house. What is the function for Johnny's distance d from Bobby's house? Bobby's Function: d = 55t Slope = 55 = Bobby's speed Johnny's speed = 55 = Slope of Johnny's Function At 11am, t = 1, and Johnny is 300 miles from Johnny's house.

miles hours Bobby Johnny Johnny at 11am

Finding the Equation of a Parallel Line In the previous story, we know Bobby's function is d = 55t. We know that Johnny's function will have the same slope, 55. We also know that at t = 1, Johnny's d = 300. To find the function, we start with the generic y-intercept form of a linear function: y = mx + b. Or, in our case: d = mt + b We then plug in what we know: m = 55, d = 300, t = 1. We get: 300 = (55)(1) + b Solving for b, we get: b = 245 So our function for Johnny is: d = 55t + 245

You Try Find the equation of the line parallel to y = -4x + 7 that passes through (2, 4). m = -4 4 = (-4)(2) + b 4 = -8 + b b = 12 So, y = -4x + 12

Finding the Equation of a Perpendicular Line Suppose we want to find the equation of a line passing through (2, 4) and perpendicular to the line y = -4x + 7. Again, the slope of our original line is -4. The slope any perpendicular line is the negative reciprocal of -4. So, m·(-4) = -1, or Plugging in the coordinates we have, we get:

You Try Find the equation of the line passing through (-3, 5) and perpendicular to y = 5x – 3. The slope of the original line is 5, so the slope of our perpendicular line is: