Parallel & Perpendicular Lines

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Presentation transcript:

Parallel & Perpendicular Lines Writing Equations of Parallel and Perpendicular Lines

Objectives Vocabulary parallel lines perpendicular lines Identify and graph parallel and perpendicular lines. Write equations to describe lines parallel or perpendicular to a given line. Vocabulary parallel lines perpendicular lines

Helpful Hint If you know the slope of a line, the slope of a perpendicular line will be the "opposite reciprocal.”

Writing Equations of Parallel and Perpendicular Lines Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 1 Find the slope of the line. y = 3x + 8 The slope is 3. The parallel line also has a slope of 3. Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form. Substitute 3 for m, 4 for x1, and 10 for y1. y – 10 = 3(x – 4)

Continued Write an equation in slope-intercept form for the line that passes through (4, 10) and is parallel to the line described by y = 3x + 8. Step 3 Write the equation in slope-intercept form. y – 10 = 3(x – 4) y – 10 = 3x – 12) Distribute 3 on the right side. y = 3x – 2 Add 10 to both sides.

Try This! Write an equation in slope-intercept form for the line that passes through (5, 7) and is parallel to the line described by y = x – 6. Step 1 Find the slope of the line. The slope is . y = x –6 The parallel line also has a slope of . Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

Try This! Continued Write an equation in slope-intercept form for the line that passes through (5, 7) and is parallel to the line described by y = x – 6. Step 3 Write the equation in slope-intercept form. Distribute on the right side. Add 7 to both sides.

Writing Equations of Parallel and Perpendicular Lines Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5. Step 1 Find the slope of the line. y = 2x – 5 The slope is 2. The perpendicular line has a slope of because Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form. Substitute for m, –1 for y1, and 2 for x1.

Step 3 Write the equation in slope-intercept form. Continued Write an equation in slope-intercept form for the line that passes through (2, –1) and is perpendicular to the line described by y = 2x – 5. Step 3 Write the equation in slope-intercept form. Distribute on the right side. Subtract 1 from both sides.

Try This! Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x. Step 1 Find the slope of the line. y = 5x The slope is 5. The perpendicular line has a slope of because . Step 2 Write the equation in point-slope form. y – y1 = m(x – x1) Use the point-slope form.

Try This! Continued Write an equation in slope-intercept form for the line that passes through (–5, 3) and is perpendicular to the line described by y = 5x. Step 3 Write in slope-intercept form. Distribute on the right side. Add 3 to both sides.

Write an equation is slope-intercept form for the line described. Try This! Write an equation is slope-intercept form for the line described. 1. contains the point (8, –12) and is parallel to 2. contains the point (4, –3) and is perpendicular to y = 4x + 5