2 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?
3 Perpendicular lines are lines in the same plane that intersect to form a right angle. The symbol for perpendicular lines isSketch 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.
4 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+3A line will be perpendicular to a vertical line if it is a horizontal line.Example: x=5 is perpendicular to y=9A line will be perpendicular to a horizontal line if it is vertical.Example: y=0 is perpendicular to x=7
5 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+bGiven m= , New m=- 2 1x=3 and y=00=- 2 1 (3)+b0=-6+b6=by=-2x+6
6 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 pointWrite the equation of the line as y=_____The y-coordinate is 1y=1 is the equation of the line
7 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 pointWrite the equation of the line as x=______The x-coordinate is 2The equation of the line is x=2