Parallel and Perpendicular Lines Honors Math – Grade 8.

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Presentation transcript:

Parallel and Perpendicular Lines Honors Math – Grade 8

Get Ready for the Lesson The graph shows the graphs of three linear equations. Describe the lines. The lines are all parallel. Examine the slope of each line. The slope of each line is the same.

KEY CONCEPT Parallel Lines in a Coordinate Plane Parallel lines have the same slope. An equation of a parallel line can be written if a point on the line and the equation of the other line are given.

Write the equation of the line in slope-intercept and standard forms that is parallel to the given equation and passes through the given point. The line parallel to y = -3x – 2 has the same slope. What is the slope of the line? m = –3 Use point-slope. Distribute. Remember slope-intercept is y = mx +b. Remember Standard Form is Ax + By = C. Add 3x to both sides

Write the equation of the line in slope-intercept and standard forms that is parallel to the given equation and passes through the given point. The line parallel to y = ¼ x + 7 has the same slope. What is the slope of the line? m = 1/4 Use point-slope. Distribute. Remember slope-intercept is y = mx +b. Remember Standard Form is Ax + By = C. Multiply both sides by 4. Subtract x from both sides.

Write the equation of the line in slope-intercept and standard forms that is parallel to the given equation and passes through the given point. The line parallel to y = 2/3 x + 7 has the same slope. What is the slope of the line? m = 2/3 Use point-slope. Distribute. Remember slope-intercept is y = mx +b. Remember Standard Form is Ax + By = C. Multiply both sides by 3. Subtract 2x from both sides. THINK

Describe the lines. The lines are all perpendicular. Examine the slope of each line. One slope is positive; one is negative; they are reciprocals.

An equation of a perpendicular line can be written if a point on the line and the equation of the other line are given. KEY CONCEPT Perpendicular Lines Perpendicular lines have slopes that are opposite reciprocals of each other.

Write the equation of the line in slope-intercept and standard forms that is perpendicular to the given equation and passes through the given point. The line perpendicular to x + 4y = 12 has the opposite reciprocal. What is the slope of the line? To find the slope of a line in standard form, use the following formula: What is the slope of the perpendicular line? Distribute. Remember slope-intercept is y = mx +b. Remember Standard Form is Ax + By = C. Subtract 4x from both sides Point- slope

Write the equation of the line in slope-intercept and standard forms that is perpendicular to the given equation and passes through the given point. The line perpendicular to y = -3/2 – 7 has the opposite reciprocal. What is the slope of the line? What is the slope of the perpendicular line? Distribute. Remember slope-intercept is y = mx +b. Remember Standard Form is Ax + By = C. Multiply both sides by 3. Point-slope THINK