graphing linear equations notes pdf

4 0 obj Graphing and Systems of Equations Packet 1 Intro. x��[mo�8� ��E��]�"�8n��]� p�E�:��Cb��rm��Pv�Fd��q�@��3��i�L��Æ�6M9W��l�4�ۿ�.�h2-��lztq��YS�''��Ͼ.�_!��gV(VW��M�.��J&%�]~=��=�.26��\%��T'u5��4K��g��T��U,͓�iO'e3N�b��8 �^"�Ԋ;�*��n!��\D��q��]�Js��lRMS��P�� stream Step 3 Draw the line through the two points. Cypress College Math Department – CCMR Notes Graphing Linear Equations, Page 4 of 10 Graph the following equations. w�ɪ,��N֥k��:��l��-�k�c�Hx�.��ɶ��Z_<4]ύ��O�@�XN@Ȇ/{$�`>�Ϝ��i��p�c�&�� Plot the x and y coordinates on the grid and complete the graph. Linear Systems: SOLVE WITH GRAPHING Guided Notes Vocabulary: System of Linear Equations two or more linear equations Solution of a System of Linear Equations an ordered pair that makes all of the equations in a system true; the point of intersection Solutions to Systems: One Solution: (-2, 2) (Where the lines intersect.) Graphing Linear Equations Coals Graph a linear equation using a table or a list of values. Graphing a Linear Equation . Before rushing to use a linear equation calculator, it is important for students to master the principles.First of all, seventh graders taking this test need to use the standard formula for linear equations to find corresponding points for x and y coordinate pairs and fill in the table provided. <> Graph horizontal and vertical lines. Each point in the coordinate plain has an x-coordinate (the abscissa) and a y-coordinate (the ordinate). Graphing A Linear Equation Algebra 6.0 To graph a Linear Equation: 1. For the table we are creating, we are allowed to pick any inputs we want. %PDF-1.3 Linear equation graph: Type 1 finds y-coordinates by replacing the x value in the specified equation. 2 0 obj Graphing Linear Equations Using Slope and Intercepts X-INTERCEPT (of a line) the point where the line intersects the x-axis MORE NOTES and EXAMPLES To find an X-intercept: To find a Y-intercept: A. Substitute the values of x in the given equation to find the y- coordinates. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. %�� 3 Change 3 to 1 RISE RUN oaaoooaooaooooaaoaoo oaaoooaoooooooaaoaoo Ex. The points on the line are called _____ of the equation. B. The point is stated as an ordered pair (x,y). To graph linear equations (using slope intercept form): 1. stream Make A TABLE . Graph linear equations: Find the missing values of type 2 x and y and complete the table. GRAPHING ODE SYSTEMS 5 Example 3.2 This time we consider the linear system below — since it is decoupled, its general solution (on the right) can be obtained easily by inspection: (12) (x′ = −x y′ = −2y x = c1 1 0 e−t +c 2 0 1 e−2t. �!�eV�. EXAMPLE 1: Graphing a Linear Equation Graph each equation using a table of values from−2≤x≤2. xŝ[��q��+��Ȃ�,h��`s"iexuٕ�ؿ�_ݺ��g��"��S��ugw��n�s��Mn��o�?y��1�s�,4m{��\�}s��7�?��ҷ�ˇz��|S��es��M��?��/߾��ӫ��/�>}��N_�/�>�Z�� SE}/#�ӏ�~��%%X�޽��~��ӗ��B�Y��h�m!k��3��=O��j%�Cjc_y��P��T��DeM�ʪ��Ee��Tv��U�mwn��1,(�k7�Gx��O�_��P�v�� ͬ�RL�� [:��;��m�.�-�_��-D��j��qt)�q�Kte)��7�_��v�s۵6��#1Í�X��V��ϋj�'YQ�u�bi��T�>�?ւ��-)�h_]?��5e��c ��x��?S�3�d�EXG��/�y��-m��o��D��je��t��=q�0/�ڣ�T'�� E)��aA|��J3P�`ɇ��o�x��w?��ۯe�v�H׶$!F��i�_|K��0��}�6�s'2L��C�ؚ,�#{_�]��[#�x��ks��q|��a�|!j�Odl�%Y�/�à�Ջ�� B�Wď�K��Rh��~�B,R��(6!�a�D,R7d�X̐X3ٜą�1��I��8�? }��G&�oGaf0��U��׬U�Bg��O�~ Qn��Lۊ��V�E�~.9�a�`��X��P�.$��S��b�s�?Z��P��$�?8��Q�4�٧DBb.��B��2��. endobj 5.5 Algebra 1 Notes Graphing Linear Functions Name Period Date Forms of a Linear Equation NAME OF EQUATION FORM OF EQUATION WHEN TO USE EQUATION Slope-Intercept Form y mx b = + m is the slope b is the y-intercept When you are given the slope and y-intercept or can find this information from a graph. Example 2: Steps Example Step 1: Make a t-chart Step 2: Pick in 3-5 values for x. 1. yx 41 2. Solving Systems of Linear Equations Graphing Student/Class Goal Students thinking about continuing their academic studies in a post-secondary institution will need to know and be able to do problems on solving systems of equations. If we want to graph a linear equation, then we will need to make a table of inputs and outputs. <> Converting it as in (5) to a single ﬁrst order ODE and solving it by separating variables J��2� �b�t�%�c��3�FW��F� ��!��4\ޥ��F�*9�ñ�G�vEI�6��&��TA�&��+̄Ĺ�t�p`%��SdfZ& LT 2.A NOTES: Graphing Linear Equations CONCEPT #0: Slope and Special Lines CONCEPT #1: Graphing in Standard Replace the x wit h zero B. 3 0 obj y intercept = 4 Step 1 The y-intercept is 4, so the line contains (0, 4). How to Graph Linear Equation y = step 1: Plot the y-intercept, b, on mx + b the graph. Step 2 Slope = -2 5 Count 2 units down and 5 units right from (0, 4) and plot another point. <>/ExtGState<>/XObject<>/ProcSet[/PDF/Text/ImageB/ImageC/ImageI] >>/MediaBox[ 0 0 612 792] /Contents 4 0 R/Group<>/Tabs/S/StructParents 0>> Solution NOTES y = mx + b (slope-intercept form) “m” is the slope “b” is the y-coordinate of the y-intercept To graph linear equations (using slope-intercept form): 1. The coordinate plane has 4 quadrants. Guided Notes: Solving Systems of Equation by Graphing Name:_____ DEFINITIONS: A system of equations is a set of _____ or more equations with the same _____. Each worksheet has nine problems with graphing linear equations. Notes on graphing 39: HW graphing linear equations Graphing Lines SI.pdf 40 Graphing linear inequalities Graphing linear inequalities Foldable.pdf 41 Graphing linear inequalities HW Day 9.3 Graphing Linear Inequalities Ho: 42 System of inequalities Graphing Systems of Inequalities Homew 43 Knowledge rating sheet We use this paper in class as the notes for graphing linear equations on a coordinate plane. Plot x and y coordinates in the grid and complete the graph. * If slope is a fraction use the + & – denominator and 0 Step 3: Substitute each value for x and y = solve for y. EX: Graph y = -5 Slope is 3. 2 4 5 yx A solution to a system of equations is a set of values for the variables that _____ all the GS. <>>> Graphing Linear Equation: Type 1. << /Length 5 0 R /Filter /FlateDecode >> To find x-intercept, let y = _____ and solve for _____. NOTES Slope-Intercept Form of a linear equation: y = mx + b Where “m” is the slope, and “b” is the y-coordina te of the y-intercept. %PDF-1.5 To Graphing Linear Equations The Coordinate Plane A. ⃣Write linear equations in slope-intercept form ⃣Draw a graph of an equation 2.3 More About Linear Functions ⃣Manipulate an expression in order to reveal and explain different properties ⃣Change the value of part of an expression and analyze how it changes the whole expression 2.4 Graphing Linear Equations 3. 20 problems for teams to solve in a relay race game. �K::3't�*2ncX��t-b@��{0Ϗ�30ܦB3�b[ǅ|�Aj@�U�rn�� PQ�wuy��d�3��6�&a��UY��7��>E�xR�� \Rb��Pdk��$ı�u\�Zͅ��P�_)��y��A��3s��A�&6x�g��.��3��z��pO��̵��\�c-|f�գn�Ǘ؂��S��$z��m2��z�C�,�fȺ��v�Uu2ݑ��4ϳWRa�$ML��~��,�t��̹҅�r.��忰pTC�l�&�K�M��;�JW< ��M� � ��Z��5xŵ��kX�`��s�7��#��հ)щF��H��'�f��@�E��a��yK��s.��d*:&��I(��3��7�_X��c�n �l#��F=C;(��%�-�l"JV9��>�Qẃ�1�娍��-��5XI�K��J��.�mP�+��t�C8�G0�bpw�V�5HU9�T��FR��{u��I&5G��hJ�$��L��x? Graph y 2x 7 Graph 2 3 2 y x Practice Plot each of the following equations on the same graph. C. Horizontal Axis is the X – Axis. Linear Equations have the basic form of Ax + By = C. Graphing Linear Equations: x and y-intercepts: x-intercepts of a graph are the x-coordinates that are common with the x-axis. Each worksheet has nine problems graphing linear equation. 1: Graph the line given the slope and y-intercept. %�� Solve simple cases by inspection. endobj A linear equation is an equation whose graph is a _____. 1. y 3x 4 2. Text Messages A wireless communication provider estimates that the number of text messages m (in millions) sent over several years can be modeled by the function m = 120t + 95 where t represents the Determine the y-intercept and plot that point on the graph. Chapter 5 - Systems of LInear Equations. Rearrange the equation so that it is in slope-intercept form 2. 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