 2.4.2 – Parallel, Perpendicular Lines

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2.4.2 – Parallel, Perpendicular Lines

We know how to quickly graph certain linear equations
Y = mx + b Slope-intercept Y-intercept as a starting point; slope to find a second point Ax + by = c Standard Form Use the x and y intercepts as the two points

Now, we will compare two lines/equations and their graphs
Two lines may be: 1) Parallel 2) Perpendicular 3) Neither

Parallel Lines Given two lines, they are considered parallel if and only if they have the same slope; m1 = m2 The lines never intersect; run off in the same direction “Air” between them

Example. Tell whether the following lines are parallel or not.
1) y = 3x + 4, y – 3x = 10 2) -4x + y = -6, y = 4x 3) y – x = 1, y = -x

Example. Graph the equation y = 3x + 4
Example. Graph the equation y = 3x + 4. Then, graph a line that is parallel and passes through the point (1, 1).

Example. Graph the equation y = -x + 5
Example. Graph the equation y = -x + 5. Then, graph a line that is parallel and passes through the point (1, 1).

Perpendicular Lines Two lines are perpendicular, if and only if, their slopes are negative reciprocals OR their product is -1 OR m1(m2) = -1 Graphically, two perpendicular lines intersect at a 90 degree angle

Example. Tell whether the following lines are perpendicular, parallel, or neither.
1) y = 3x + 4, y = (-1/3)x – 5 2) y = 4x – 5, y = x 3) y = (x/2) – 9, y + (2/x) = -6 4) y = x – 1, y = -x

Example. Graph the equation y = 3x + 4
Example. Graph the equation y = 3x + 4. Then, graph a line that is perpendicular and passes through the point (1, 1).

Example. Graph the equation y = -x + 5
Example. Graph the equation y = -x + 5. Then, graph a line that is perpendicular and passes through the point (1, 1).

Horizontal and Vertical Lines
Horizontal Lines = lines of the form y = a; must have a “y-intercept” Vertical Lines = lines of the form x = a; must have a “x-intercept” General Rule; must be able to see the line, so cannot draw a line on top of the axis

Example. Graph the equation x = 3.

Example. Graph the equation y = -4.

Assignment Pg. 91 33-49 odd, 50-53, 60, 62, 69, 70