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Linear Equations: Parallel and Perpendicular Lines

Learn how to identify and write equations of parallel and perpendicular lines using slope. Practice problems included.

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Linear Equations: Parallel and Perpendicular Lines

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  1. Do Now 11/16/18 • Take out HW from last night. • Text p. 185, #4-30 evens, 40 • Copy HW in your planner. • Text p. 191, #4-28 evens, 32-35 all • Quiz sections 4.1-4.3 Tuesday • In your notebook, answerthefollowing. Useyourknowledge of slopetoexplainhowyoucandetermineif 2 lines are parallel bylooking at theirgraphs. Write anequation parallel to y = 3x + 1. Canthesameprocessbeusedtowriteanequation of a perpendicular line? Write anequation of a perpendicular line to y = 3x + 1. (Draw a graphto help you.)

  2. Homework Text p. 185, #4-30 evens, & 40

  3. Learning Goal • Students will be able to write linear functions. Learning Target • Students will be able to identify and write equations of parallel and perpendicular lines

  4. Section 4.3 “Writing Equations of Parallel and Perpendicular Lines” • PARALLEL LINES • If two nonvertical lines in the same plane have the same slope, then they are parallel. • If two nonvertical lines in the same plane are parallel, then they have the same slope.

  5. Write an equation of the line that passes through (–3,–5) and is parallel to the liney = 3x – 1. STEP1 Identify the slope. The graph of the given equation has a slope of 3. So, the parallel line through (– 3, -5) has a slope of 3. STEP 2 Substitute for the slope and the coordinates of the given point in Write point-slope form. Substitute 3 for m, -3 for x, and -5 for y. Write an equation of the line in slope-intercept form. STEP3 Distributive property. Simplify. Write in slope-intercept form.

  6. Write an equation of the line that passes through (–2,11)and is parallel to the liney= -x + 5. STEP1 Identify the slope. The graph of the given equation has a slope of -1. So, the parallel line through (– 2, 11) has a slope of -1. STEP 2 Substitute for the slope and the coordinates of the given point in Write point-slope form. Substitute -1 for m, -2 for x, and 11 for y. Write an equation of the line in slope-intercept form. STEP3 Distributive property. Simplify. Write in slope-intercept form.

  7. PERPENDICULAR LINES • If two nonvertical lines in the same plane have slopes that are negative reciprocals, then the lines are perpendicular. • If two nonvertical lines in the same plane are perpendicular, then their slopes are negative reciprocals ½ and -2 are negative reciprocals. 3 and -1/3 are negative reciprocals.

  8. Determine which lines, if any, are parallel or perpendicular. – x y = + 1 2 1 5 5 5 x – y = Line a: y = 5x – 3 Line b:x +5y = 2 Line c:–10y – 2x = 0 Find the slopes of the lines. Write the equations for lines a, b, and cin slope-intercept form. Linea: y = 5x – 3 Lineb: x + 5y = 2 Linec: – 10y – 2x = 0 5y = – x + 2 – 10y = 2x Lines band chave slopes of –1/5, so they are parallel. Linea has a slope of 5, the negative reciprocal of –1/5, so it is perpendicular to lines band c.

  9. Determine which lines, if any, are parallel or perpendicular. 1 1 3 2 – – x y = Line a: 2x + 6y = -3 Line b:3x – 8 = y Line c:–1.5y + 4.5x = 6 Find the slopes of the lines. Write the equations for lines a, b, and cin slope-intercept form. 2x + 6y = -3 3x – 8 = y –1.5y + 4.5x = 6 Linea: Lineb: Linec: – 1.5y = -4.5x + 6 6y = –2x – 3 y = 3x – 4 Lines band chave slopes of 3, so they are parallel. Linea has a slope of -1/3, the negative reciprocal of 3, so it is perpendicular to lines band c.

  10. y= mx+ b 1 – (4) + b – 5= Substitute – for m, 4 for x, and – 5 for y. 2 Identify the slope. The graph of the given equation has a slope of 2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (4, –5) is -1/2 . 1 2 – 3= b 1 2 1 y = – x – 3 Substitute – formand–3for b. 2 Write an equation of the line that passes through(4, – 5)and is perpendicular to the liney = 2x + 3. STEP1 STEP 2 Find the y-intercept. Use the slope and the given point. Write slope-intercept form. Solve for b. STEP3 y = m x + b Write slope-intercept form. Write an equation.

  11. Identify the slope. The graph of the given equation has a slope of 1/2. Because the slopes of perpendicular lines are negative reciprocals, the slope of the perpendicular line through (-3, 1) is -2 . Write an equation of the line that passes through(-3, 1)and is perpendicular to the liney = ½x + 3. STEP1 Substitute for the slope and the coordinates of the given point in STEP 2 Write point-slope form. Substitute -2 for m, -3 for x, and 1 for y. Write an equation of the line in slope-intercept form. STEP3 Distributive property. Simplify. Write in slope-intercept form.

  12. The position of a helicopter search and rescue crew is shown in the graph. The shortest flight path to the shoreline is one that is perpendicular to the shoreline. Write an equation that represents this path.

  13. Homework • Text p. 191, #4-28 evens, 32-35 all

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