3.2 Understanding how equations are represented on a graph  (Page 4/4)

• 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

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) ( $\frac{4}{3}$ ; 0)

4.2 (0 ; –2½) (7½ ; 0)

4.3 (0 ; 0) (0 ; 0)

4.4 (0 ; $-\frac{5}{3}$ ) ( $\frac{5}{4}$ ; 0)

4.5 (0 ; –4) ( $\frac{4}{3}$ ; 0)

4.6 (0 ; ½) (–½ ; 0)