Five-Minute Check (over Lesson 4 3) CCSS Perpendicular .

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Five-Minute Check (over Lesson 4–3)CCSSThen/NowNew VocabularyExample 1: Parallel Line Through a Given PointExample 2: Real-World Example: Slopes ofPerpendicular LinesExample 3: Parallel or Perpendicular LinesExample 4: Parallel Line Through a Given PointConcept Summary: Parallel and Perpendicular Lines

Over Lesson 4–3What is the point-slope form of an equation for aline that passes through the point (5, –5) with theslope m 2?A. y 2x 5B. y 2x – 5C. y 5 2(x – 5)D. y 2(x – 5)

Over Lesson 4–3

Over Lesson 4–3What is the point-slope form of an equation for a linethat passes through the point (–1, 5) with the slopem A.B.C.D.?

Over Lesson 4–3A.B.C.D.

Over Lesson 4–3A. What is the standard form of the equation of thediagonal AC?A. x 10y 18B. x 5y 9C. 10x y 18D. x – 10y 9

Over Lesson 4–3B. What is the slope-interceptform of the equationof the diagonal AC?A. 10y 18 – xB.C.D. y 18 – x

Over Lesson 4–3Which equation has a graph that passes throughthe points at (3, 4) and (–1, –4)?A. y – 3 2(x – 4)B. y 1 2(x 4)C. y 4 2(x – 1)D. y – 4 2(x – 3)

Content StandardsF.LE.2 Construct linear and exponential functions,including arithmetic and geometric sequences, givena graph, a description of a relationship, or two inputoutput pairs (include reading these from a table).S.ID.7 Interpret the slope (rate of change) and theintercept (constant term) of a linear model in thecontext of the data.Mathematical Practices5 Use appropriate tools strategically.Common Core State Standards Copyright 2010. National Governors Association Center for Best Practices and Council of Chief StateSchool Officers. All rights reserved.

You wrote equations in point-slope form. Write an equation of the line that passesthrough a given point, parallel to a given line. Write an equation of the line that passesthrough a given point, perpendicular to agiven line.

parallel lines perpendicular lines

Parallel Line Through a Given PointWrite the slope-intercept form of an equation forthe line that passes through (4, –2) and is parallel tothe graph of

Parallel Line Through a Given PointPoint-slope formReplace m withy1 with –2, and x1 with 4.Simplify.Distributive PropertySubtract 2 from each side.

Parallel Line Through a Given PointWrite the equation inslope-intercept form.Answer: The equation is

Write the slope-intercept form of an equation for theline that passes through (2, 3) and is parallel to thegraph ofA.B.C.D.

Perpendicular Line Through a Given PointWrite an equation in slope-intercept form for theline that passes through (4, –1) and isperpendicular to the graph of 7x – 2y 3.Step 1Find the slope of the given line by solving theequation for y.7x – 2y 3Original equation7x – 7x – 2y –7x 3–2y –7x 3Subtract 7x from each side.Simplify.Divide each side by –2.Simplify.

Perpendicualar Line Through a Given PointThe slope isStep 2The slope of the perpendicular line is theopposite reciprocal ofFind the equation ofthe perpendicular line.y – y1 m(x – x1)Point-slope formSimplify.

Perpendicualar Line Through a Given PointDistributive PropertySubtract 1 from eachside.Simplify.Answer:

Write an equation in slope-intercept form for theline that passes through (–3, –2) and isperpendicular to the graph of x 4y 12.A.B.C.D.

Homework:Pg 243 #11-15 odd,23-27 odd

Slopes of Perpendicular LinesA. GEOMETRY The height ofa trapezoid is the length of asegment that is perpendicularto both bases. In trapezoidARTP, RT and AP are bases.Can EZ be used to measurethe height of the trapezoid?Explain.

Slopes of Perpendicular LinesFind the slope of each segment.Answer: The slope of RT and AP is 1 and the slope ofEZ is –7. Since 1(–7) –1, EZ is not perpendicular to RTand AP. So, it cannot be used to measure the height ofARTP.

Slopes of Perpendicular LinesB. GEOMETRY The height of a trapezoid is thelength of a segment that is perpendicular to bothbases. In trapezoid ARTP, RT and AP are bases. Arethe bases parallel?Answer: Yes, both RT and AP have a slope of 1.

The graph shows thediagonals of a rectangle.Determine whether JL isperpendicular to KM.A. JL is not perpendicular to KM.B. JL is perpendicular to KM.C. cannot be determined

Parallel or Perpendicular LinesDetermine whether the graphs of 3x y 12,and 2x – 6y –5 are parallel orperpendicular. Explain.Graph each line on a coordinate plane.

Parallel or Perpendicular LinesAnswer: From the graph, you cansee thatis parallel to2x – 6y –5. They are parallelbecause they have equal slopes.3x y 12 is perpendicular to themboth because the product of theirslopes,and –3, is –1.

Determine whether the graphs of y –2x 1,x – 2y –4, and y 3 are parallel or perpendicular.A. y –2x 1 and x – 2y –4 areperpendicular. None of thelines are parallel.B. y –2x 1 and y 3 areperpendicular. None of thelines are parallel.C. y –2x 1 and x – 2y –4 areparallel. None of the lines areperpendicular.D. None of the lines are parallelor perpendicular.

A. y –2x 1 and x –2y –4 are perpendicular. None of the lines are parallel. B. y –2x 1 and y 3 are perpendicular. None of the lines are parallel. C. y –2x 1 and x –2y –4 are parallel. None of the lines are perpendicular. D. None of the lines are parallel or perpendicul

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