Page 152 - Mathematics GRADE 9, DE-STREAMED (MTH1W)

• What do you notice about the slope of a graph that is rotated 180° about the origin compared to the slope of the original graph?
Sample Tasks
1. Provide students with the graph of a line y = ax for a given value of a on a grid. Provide tools such as tracing paper, rulers, and Miras, and have students perform translations, rotations, and reflections on the graph and describe how each transformation affects the graph.
2. Have students use graphing technology to explore the effects of various transformations on the line y = ax for a chosen value of a. Have them explore which transformations are connected to each of the following changes in the equation:
• y=ax+b
• y=a(x−c)
• y=−ax
• y=–1x a
3. Have students rotate the line y = ax, for a chosen value of a, clockwise or counterclockwise by 90°. Have them compare the slopes of these lines and discuss how the slopes of perpendicular lines are related. Their rotation might look something like the animation below:
4. Have students translate the line y = ax up or down for a chosen value of a. Have them compare the slopes of these lines and discuss how the slopes of parallel lines are related.
C4.4 Characteristics of Linear and Non-Linear Relations
determine the equations of lines from graphs, tables of values, and concrete representations of linear relations by making connections between rates of change and slopes, and between initial values and y- intercepts, and use these equations to solve problems
Teacher supports
Examples
• determining the equation of lines from representations: o from a graph:
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