Are You Ready? Slopes of Parallel and Perpendicular Lines

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1 SKLL 6 Are You Read? Slopes of Parallel and Perpendicular Lines Teaching Skill 6 Objective Determine when a pair of lines is parallel or perpendicular. Remind students that the slope of a line determines how steep or how flat the line is. Draw a pair of parallel lines on the board. Ask: What would ou sa is true about the steepness of the two lines? (The steepness is the same.) plain that this is true for ever pair of parallel lines; the steepness is the same so the slopes are equal. Work through the first eample with students. Net, draw a pair of perpendicular lines on the board and eplain that the slopes are negative reciprocals. Give several eamples of negative reciprocals. Tell students that it is eas to find the slope of a line written in slope-intercept form, so if the line is written in an other form, rewrite it in slope-intercept form. Then work through the second eample with students. PRACTC ON YOUR OWN n eercises, students determine whether a pair of lines is parallel or perpendicular. Alternative Teaching Strateg Objective Graph a pair of lines to determine whether the are parallel, perpendicular, or neither. Some students ma benefit from visualizing wh equal slopes produce parallel lines. Present the following equations: Have students graph the two lines on the same coordinate plane using the -intercept and the slope. Remind students that a slope of means rise and run and that the -intercept indicates where to place the beginning point. Students graphs should look like the following: CHCK Determine that students know how to determine whether a pair of lines is parallel or perpendicular. Students who successfull complete the Practice on Your Own and Check are read to move on to the net skill. COON RRORS Students ma incorrectl identif two lines as being perpendicular when their slopes are reciprocals, rather than negative reciprocals. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, ma benefit from the Alternative Teaching Strateg. Ask: What kind of lines are these? (parallel) Have students repeat the eercise for several sets of parallel lines. When complete, ask: What is true about ever pair of parallel lines? (The have equal slopes.) Net, have students graph the following lines on the same coordinate plane: and. Point out that the slopes of the two lines are negative reciprocals. Ask: What kind of lines are these? (perpendicular lines) Have students graph several sets of perpendicular lines to arrive at the conclusion that lines with negative reciprocal slopes are perpendicular. Finall, have students graph a pair of lines that is neither parallel nor perpendicular. plain that these lines are intersecting lines, but not perpendicular. Copright Holt cdougal. 6 Álgebra stás listo? ntervención enriquecimiento

2 Nombre Fecha Clase DSTRZA 6 stás listo? Pendientes de líneas paralelas perpendiculares Líneas paralelas Si dos líneas son paralelas, tienen la misma pendiente. Por lo tanto, si dos líneas tienen la misma pendiente, son paralelas. jemplo : Recuerda: Cuando una ecuación está epresada como m b, el coeficiente de es la pendiente. Como la pendiente de ambas líneas es, las líneas son paralelas. Líneas perpendiculares Si dos líneas son perpendiculares, sus pendientes son recíprocos negativos. Por lo tanto, si dos líneas tienen pendientes que son recíprocos negativos, son perpendiculares. jemplo : 8 Primero, vuelve a escribir la segunda ecuación en forma de pendiente-intersección: 8. La pendiente de la primera línea es la pendiente de la segunda línea es. Como son recíprocos negativos, las líneas son perpendiculares. ndica si las ecuaciones lineales de cada par son paralelas, perpendiculares o ninguna de las dos opciones ndica si las ecuaciones lineales de cada par son paralelas, perpendiculares o ninguna de las dos opciones Copright Holt cdougal. 6 Álgebra stás listo? ntervención enriquecimiento

3 SKLL 8 Are You Read? Function Tables Teaching Skill 8 Objective Generate ordered pairs for given values of a function. plain to students that function tables are used to generate ordered pairs in the form (, ). These ordered pairs can be used to graph a function. Review with students how to evaluate a function for a given value of. Remind students that the should be particularl careful when substituting negative values into a function. Direct students attention to the eample. Point out that the -values are called inputs. Ask: n this eample, what are the inputs? (,,, and ) plain that the inputs are substituted into the function, and the -values that result are called the outputs. The ordered pairs are the points (, ). Work through the eample, making sure students understand how the function is being applied to the input values to generate the outputs. Then have students complete the practice eercises. PRACTC ON YOUR OWN n eercises 8, students generate ordered pairs b completing function tables for given inputs. CHCK Determine that students know how to complete function tables. Students who successfull complete the Practice on Your Own and Check are read to move on to the net skill. COON RRORS Students ma not perform the operations of a function s rule correctl and ma arrive at an incorrect output for a given input. Students who made more than errors in the Practice on Your Own, or who were not successful in the Check section, ma benefit from the Alternative Teaching Strateg. Alternative Teaching Strateg Objective Generate ordered pairs for given values of a function. Some students ma need additional practice evaluating functions. Remind students that when ou evaluate a function, ou appl a rule to an input value to generate an output. Understanding the rule that is being applied is critical to completing a function table. Write the following function table on the board and have students cop it on their paper. ( ) ( ) ( ) ( ) ( ) Have students consider the rule that is being applied to the input values,,,,, and. Have a volunteer tr to write an algebraic epression that represents the rule. Guide the volunteer if needed. ( ) Then have students write the function in the center column of the table and complete the function table. Have students work in pairs for the net part of the eercise. nstruct each student to write down a function (rule) in the form of an algebraic epression (e.g. 6), but not show their partner. ach student should then create a function table similar to the one above for their function. The should use boes, rather than variables, as above. When the have created their tables, the should echange papers, tr to figure out their partner s rule, and then complete the table. Repeat the eercise until ou feel comfortable that students understand how to complete function tables. Copright Holt cdougal. 6 Álgebra stás listo? ntervención enriquecimiento

4 Nombre Fecha Clase DSTRZA 8 stás listo? Tablas de funciones Una tabla de función es un conjunto de soluciones para una ecuación. Cuando se da un conjunto de valores de, sustitue los valores en la ecuación para hallar los valores correspondientes de. Usa los valores de e para generar pares ordenados. jemplo: Genera pares ordenados para la función para,,,,. () 8 () () () () 8 8 Genera pares ordenados para cada función para,,,, ( ) 8. ( ) Genera pares ordenados para cada función para,,,,..... ( ) Copright Holt cdougal. 68 Álgebra stás listo? ntervención enriquecimiento

5 Nombre Fecha Clase CAPÍTULO nriquecimiento Números perfectos Un número perfecto es un número que es la suma de sus propios factores positivos (ecepto el propio número). Por ejemplo, los siguientes números son perfectos: l próimo número perfecto es 88. Cuál es el quinto número perfecto? Para hallar la respuesta, resuelve cada ecuación escribe tu respuesta en los espacios en blanco al final de la página ( ) 6. ( ) ,..., Copright Holt cdougal. Álgebra stás listo? ntervención enriquecimiento

6 Respuestas, continuación DSTRZA 6: RSPUSTAS. perpendiculares. paralelas. perpendiculares. ninguna de las dos opciones. paralelas 6. ninguna de las dos opciones. perpendiculares 8. perpendiculares. perpendiculares. perpendicular. paralelas. paralelas. paralelas DSTRZA 8: RSPUSTAS... ninguna de las dos opciones. perpendiculares DSTRZA : RSPUSTAS Copright Holt cdougal. Álgebra stás listo? ntervención enriquecimiento

7 Respuestas, continuación Los números del al 8 están indicados con letras. C A D F B DSTRZA : RSPUSTAS Los números del al están indicados con letras. J H B F K D C L A G DSTRZA 8: RSPUSTAS... Copright Holt cdougal. Álgebra stás listo? ntervención enriquecimiento

8 nriquecimiento: Respuestas Capítulo : Todo tipo de números 8 T D 6 T R Q U N T O S C S T L R C N T É S A S C S Q N C D É C A S S U U D O S 6 D É C U A R T O N N N É P V T C T C T R N T A C U A R N T A O C H O S N T R S Capítulo : A ordenar!. ( ) 6. ( ) 6 8. ( 6 ) (6 ) 6. (6 ) Capítulo : l cuadrado mágico La suma mágica es. 8 Capítulo : Coordinación Greatest Common Factor Capítulo : Números perfectos,,6 Capítulo 6: A multiplicar. 6, T.,.,., R., U 6., S., Y 8. 8, B., O. 8, D., P., V Distributive Propert Capítulo : anía de fracciones, decimales porcentajes Bo do have problems! Capítulo 8: La potencia de pi Copright Holt cdougal. Álgebra stás listo? ntervención enriquecimiento