Page 57 - Math 9-10 (2009)

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THE ONTARIO CURRICULUM, GRADES 9 AND 10: MATHEMATICS
Modelling Linear Relations
Overall Expectations
By the end of this course, students will:
• manipulateandsolvealgebraicequations,asneededtosolveproblems;
• graph a line and write the equation of a line from given information;
• solvesystemsoftwolinearequations,andsolverelatedproblemsthatarisefromrealistic situations.
Specific Expectations
Manipulating and Solving Algebraic Equations
By the end of this course, students will:
– solve first-degree equations involving one variable, including equations with frac- tional coefficients (e.g. using the balance analogy, computer algebra systems, paper and pencil) (Sample problem: Solve
+ 4 = 3x – 1 and verify.);
– determine the value of a variable in the first degree, using a formula (i.e., by isolating the variable and then substituting known values; by substituting known values and then solving for the variable) (e.g., in analytic geometry, in measurement) (Sample problem: A cone has a volume of 100 cm3. The radius of the base is 3 cm. What is the height of the cone?);
– express the equation of a line in the form y = mx + b,given the form Ax+By+C=0.
Graphing and Writing Equations of Lines
By the end of this course, students will:
– connect the rate of change of a linear rela- tion to the slope of the line, and define
the slope as the ratio m = ;
– identify, through investigation, y = mx + b
as a common form for the equation of a straight line, and identify the special cases x = a, y = b;
– identify, through investigation with tech- nology, the geometric significance of m and b in the equation y = mx + b;
– identify, through investigation, properties of the slopes of lines and line segments (e.g., direction, positive or negative rate of change, steepness, parallelism), using graphing technology to facilitate investiga- tions, where appropriate;
– graph lines by hand, using a variety of techniques (e.g., graph x – 4
using the y-intercept and slope; graph 2x + 3y = 6 using the x- and y-intercepts);
– determine the equation of a line, given its graph, the slope and y-intercept, the slope and a point on the line, or two points on the line.
Solving and Interpreting Systems of Linear Equations
By the end of this course, students will:
– determine graphically the point of inter- section of two linear relations (e.g., using graph paper, using technology) (Sample problem: Determine the point of intersec-
x
2
rise
run
tionofy+2x=–5and
x + 3,
using an appropriate graphing technique, and verify.);
y=
y=
2 3
2 3