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Perpendicular Lines Linear Equations

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**I can find the equation of a line parallel to a given line passing through a given point.**

Essential Question: Do you use the x- or y-coordinate to find the equation parallel to x=8? How do you know?

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**Perpendicular lines are lines in the same plane that intersect to form a right angle.**

The symbol for perpendicular lines is Sketch two perpendicular lines. (Be sure to show they intersect to form a right angle by putting a box in the angle) You can determine if two lines are perpendicular by comparing their slopes.

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**When will lines be perpendicular?**

Non-vertical and non-horizontal lines have slopes that are opposite reciprocals. This means you change the sign and flip it. These lines can have the same y-intercepts, but do not need to. Example: y=2x+3 is perpendicular to y=− 1 2 x+3 A line will be perpendicular to a vertical line if it is a horizontal line. Example: x=5 is perpendicular to y=9 A line will be perpendicular to a horizontal line if it is vertical. Example: y=0 is perpendicular to x=7

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Steps to write equation a line perpendicular to a non-vertical, non-horizontal line passing through a given point. Example: find the equation of the line perpendicular to y= 1 2 𝑥+3 that passes through the point (3, 0) Find the slope of the given line. The slope of your new line will be the opposite reciprocal of this. Determine x and y from the given point. Substitute m, x and y into the equation y=mx+b and solve for b. Substitute your m and b into y=mx+b Given m= , New m=- 2 1 x=3 and y=0 0=- 2 1 (3)+b 0=-6+b 6=b y=-2x+6

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**y=1 is the equation of the line**

Steps to write the equation of the line parallel to a vertical line example: find the equation of a line parallel to x=5 that passes through (2, 1) Determine the y-coordinate of the point Write the equation of the line as y=_____ The y-coordinate is 1 y=1 is the equation of the line

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**The equation of the line is x=2**

Steps to find the equation of a line perpendicular to a horizontal line passing through a given point example: find the equation of a line perpendicular to y=7 that passes through the point (2,3) Determine the x-coordinate of the given point Write the equation of the line as x=______ The x-coordinate is 2 The equation of the line is x=2

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