Parallel and Perpendicular lines I can write an equation of a line that passes through a given point, either parallel or perpendicular to a given line.

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Presentation transcript:

Parallel and Perpendicular lines I can write an equation of a line that passes through a given point, either parallel or perpendicular to a given line.

What are parallel lines? Lines in the same plane that do not intersect are called parallel lines. What do you think is true about the slopes of parallel lines? The slopes are equal.

What is the slope of a line parallel to the given line? What is the slope of the given line? m = 2 What is the slope of a line parallel to the given line? m = 2

2 forms to write linear equations. 1. Slope-intercept form.y = mx + b m = slopeb= y-intercept 2. Point-slope form.

Write an equation in slope-intercept form for the line that passes through (-3, 5) and is parallel to the graph of y = 2x – 4. Slope =___ in the given line. y = m(x – x 1 ) + y 1 y = (x – ) y = 2 (x + 3) + 5 Slope = ___ in the new line parallel to y = 2x – y = 2x y = 2x + 11

Write an equation in slope-intercept form for the line that passes through (1, 3) and is parallel to the graph of -4x + y = – 5. Slope = ___ in the given line. y = m(x – x 1 ) + y 1 y = (x – )+ 314 Slope = ____ in the new line parallel to -4x + y = y = 4x y = 4x - 1 y =4x - 5

What are Perpendicular lines? Lines that intersect at right angles are called perpendicular lines. What do you think is true about the slopes of perpendicular lines? The slopes of perpendicular lines are opposite reciprocals of each other.

Examples of Reciprocals: Examples of Opposite reciprocals

What is the slope of a line perpendicular to the given line? What is the slope of the given line? m = 2 What is the slope of a line perpendicular to the given line? m = - ½

Write an equation in slope-intercept form for the line that passes through (2, 3) and is perpendicular to the graph of y = ⅓ x – 5. Slope = ___ in the given line. y = m(x – x 1 ) + y 1 y = (x – )+32-3 Slope = ____ in the new line perpendicular to y = ⅓ x - 5. ⅓ -3 y = -3x y = -3x + 9

Write an equation in slope-intercept form for the line that passes through (-6, 4) and is perpendicular to the graph of 2x + y = 5 Slope = _____ in the given line. y = m(x – x 1 ) + y 1 y = (x – )+ 4-6½ Slope = ___ in the new line perpendicular to 2x + y = 5 -2 y =½ x y = ½ x + 7 y = ½ (x + 6 ) + 4 ½ y = -2x + 5

homework WS: review of 5.6

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