1.4: equations of lines M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or.

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1.4: equations of lines M(G&M)–10–9 Solves problems on and off the coordinate plane involving distance, midpoint, perpendicular and parallel lines, or slope. GSE G.GPE.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point). CCSS:

Slope Formula The slope of a line through the points (x 1, y 1 ) and (x 2, y 2 ) is as follows: y2 – y1y2 – y1x2 – x1x2 – x1y2 – y1y2 – y1x2 – x1x2 – x1 m =

Understanding Slope Two (non-vertical) lines are parallel if and only if they have the same slope. (All vertical lines are parallel.)

Understanding Slope The slope of AB is: The slope of CD is: Since m 1 =m 2, AB || CD

Perpendicular Lines ( ┴ )Perpendicular Lines- 2 lines that intersect forming 4 right angles Right angle

Slopes of  Lines In a coordinate plane, 2 non vertical lines are  iff the product of their slopes is -1. This means, if 2 lines are  their slopes are opposite reciprocals of each other; such as ½ and -2. Vertical and horizontal lines are  to each other.

Example Line l passes through (0,3) and (3,1). Line m passes through (0,3) and (-4,-3). Are they  ? Slope of line l = Slope of line m = l  m Opposite Reciprocals!

Line Graphing Animation

Equation of a line in slope intercept form (y = mx+b) Now that we know how to find slope given any two points, we can generate an equation of the line connecting the two points. Example : points (3,2) and (6,9)

2 nd example

Slope-Intercept Form (y = mx+b) Find the equation of a line passing through the points P(0, 2) and Q(3, –2). Is this line parallel to a line with the equation

a) Find the equation of a line that passes through the point G ( -4, 5) and is perpendicular to b) Write the equation of a line that passes through point P (1, -2) and is parallel the line that passes through points A (-4,6) and B ( 4,10)

What is the equation of a line that models a line that is perpendicular to and goes through the point (6,6) ?

Homework

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