Warm-upWarm-up 1. Write the equation of a line given m = 1/4 and thru the point (12,-6). 2. Write the equation of a line thru these two points. A(6,15)

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Warm-upWarm-up 1. Write the equation of a line given m = 1/4 and thru the point (12,-6). 2. Write the equation of a line thru these two points. A(6,15) and B(-12, 12). 3.Write the equation of a line that is parallel to y = 2x – 3 thru this point. A(-2,7). HW: WS 7.1B Answers: 1. y = 1/4x y = 1/6 x y = 2x + 11

Lesson 7.1B Writing equations for lines that are perpendicular to a given line.

Perpendicular Slopes are opposite reciprocals. Original 1/8 -3 Opposite reciprocal -8 1/3

More Examples: Find the slope of the given line and then find the slope of any lines perpendicular to that line. m = 7 m = 3/2 m = -1

Parallel, Perpendicular, Coinciding, or intersecting but not perpendicular? 4) Y = 2x + 25) Y = 3x -6 Y = 2x - 2 Y = x 6) 7) y = 5x - 8 y = 3x + 7 m = 2, m = 2 parallelm = 3/1, m= 3/1 coinciding m = -1/5, m = 5/1 perpendicular m = 2/3, m= 3/1 intersecting

Example 1: Write the equation of the line that is perpendicular to y = 2x – 3 and goes through (6, -4) Original m = 2, opposite reciprocal m = -1/2 -4 = -1/2(6) + b -4= -3 + b -1 = b Y = -1/2 x – 1 Step 1: Find the slope. Step 2. Substitute given x, y into the equation. Step 3: Solve for b. Step 4: Substitute m and b into the equation. Y = ___x + ___.

Example 2 : Write the equation of the line that is perpendicular to y = -4/5x + 3 and goes through the point (-8, 2) Step 1: Find the slope. Step 2. Substitute given x, y into the equation. Step 3: Solve for b. Step 4: Substitute m and b into the equation. Y = ___x + ___.. Original m = -4/5, opposite reciprocal m = 5/4 2 = 5/4 ( -8) + b 2 = -10+ b 12 = b Y = 5/4x + 12

Summary: What is the difference between parallel and perpendicular slopes when writing equations of lines?