Page 35 - Math 9-10 (2009)

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THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICS
Analytic Geometry
Overall Expectations
By the end of this course, students will:
• determine the relationship between the form of an equation and the shape of its graph with respect to linearity and non-linearity;
• determine,throughinvestigation,thepropertiesoftheslopeandy-interceptofalinear relation;
• solve problems involving linear relations.
Specific Expectations
Investigating the Relationship
Between the Equation of a Relation
and the Shape of Its Graph
By the end of this course, students will:
– determine, through investigation, the char- acteristics that distinguish the equation of a straight line from the equations of non- linear relations (e.g., use a graphing calcu- lator or graphing software to graph a vari- ety of linear and non-linear relations from their equations; classify the relations according to the shapes of their graphs; connect an equation of degree one to a linear relation);
– identify, through investigation, the equa- tion of a line in any of the forms
y = mx + b, Ax + By + C = 0,
x = a, y = b;
– express the equation of a line in the form y = mx + b, given the form
Ax + By + C = 0.
Investigating the Properties of Slope
By the end of this course, students will:
– determine, through investigation, various formulas for the slope of a line segment or
a line (e.g., m = rise , or run
– identify, through investigation with tech- nology, the geometric significance of m andbintheequationy=mx+b;
– determine, through investigation, connec- tions among the representations of a con- stant rate of change of a linear relation (e.g., the cost of producing a book of pho- tographs is $50, plus $5 per book, so an equation is C = 50 + 5p; a table of values provides the first difference of 5; the rate of change has a value of 5, which is also the slope of the corresponding line; and
5 is the coefficient of the independent variable, p, in this equation);
– identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism, perpendicu- larity), using graphing technology to facil- itate investigations, where appropriate.
Using the Properties of Linear Relations to Solve Problems
By the end of this course, students will:
– graph lines by hand, using a variety
of techniques (e.g., graph y = x – 4
using the y-intercept and slope; graph 2x+3y=6usingthex-and y-intercepts);
– determine the equation of a line from information about the line (e.g., the slope and y-intercept; the slope and a point; two
∆y m = ∆x ,
), and use the formulas
m=
y2 – y1
m=
the change in x
x2 – x1
to determine the slope of a line segment or a line;
the change in y
2 3