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  • With all the advice above, you should be able to figure out the equations of these twelve graphs. If not, the next section will help.

Assessment

LO 2
Patterns, Functions and AlgebraThe learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.
We know this when the learner:
2.1 investigates, in different ways, a variety of numeric and geometric patterns and relation­ships by representing and generalising them, and by explaining and justifying the rules that generate them (including patterns found in nature and cultural forms and patterns of the learner’s own creation;
2.2 represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using:
2.2.1 verbal descriptions;
2.2.2 flow diagrams;
2.2.3 tables;
2.2.4 formulae and equations;
2.3 constructs mathematical models that repre­sent, describe and provide solutions to pro­blem situations, showing responsibility to­ward the environment and health of others (including problems within human rights, social, economic, cultural and environmental contexts);
2.4 solves equations by inspection, trial-and-improvement or algebraic processes (additive and multiplicative inverses, and factorisa­tion), checking the solution by substitution;
2.5 draws graphs on the Cartesian plane for given equations (in two variables), or deter­mines equations or formulae from given graphs using tables where necessary;
2.6 determines, analyses and interprets the equivalence of different descriptions of the same relationship or rule presented:
2.6.1 verbally;
2.6.2 in flow diagrams;
2.6.3 in tables;
2.6.4 by equations or expressions;
2.6.5 by graphs on the Cartesian plane in order to select the most useful represen­ta­tion for a given situation;
2.8 uses the laws of exponents to simplify expressions and solve equations;
2.9 uses factorisation to simplify algebraic expressions and solve equations.

Memorandum

Equations and graphs

  • From the first exercise on the six equations, the most important teaching points are: the steepness of the slopes (both positive and negative ) of the graphs; the y-intercept, and the fact that these can be deduced very easily from the equation in the standard form. The learners should be led to deduce that one needs to know only two points on a straight-line graph to be able to draw the graph.
  • As these six graphs are repeatedly used, the educator has to ensure that the learners’ work is correct for the subsequent exercises.
  • To read the gradient from a right-angled triangle, choose usable corners to draw the two sides from; also the larger the triangle, the more accurate the values.

Graphs from equations

1.1 y = –2 x + 3; m = –2 and c = 3

1.2 y = 2 x + 3; m = 2 and c = 3

1.3 y = ½ x ; m = ½ and c = 0

1.4 y = 4; m = 0 and c = 4

The gradient is read off from a graph in this section; the learners need to get an intuitive feel for the gradient from looking at it on a graph. Later we calculate it from two given points.

3.1 to 3.4 The memo is left to the teachers ingenuity.

4.1 (0 ; 1) ( 4 3 size 12{ { {4} over {3} } } {} ; 0)

4.2 (0 ; –2½) (7½ ; 0)

4.3 (0 ; 0) (0 ; 0)

4.4 (0 ; 5 3 size 12{ - { {5} over {3} } } {} ) ( 5 4 size 12{ { {5} over {4} } } {} ; 0)

4.5 (0 ; –4) ( 4 3 size 12{ { {4} over {3} } } {} ; 0)

4.6 (0 ; ½) (–½ ; 0)

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Source:  OpenStax, Mathematics grade 9. OpenStax CNX. Sep 14, 2009 Download for free at http://cnx.org/content/col11056/1.1
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