Program of Studies

6.1 Express a linear relation in different forms, and compare the graphs.
6.2 Rewrite a linear relation in either slope–intercept or general form.
6.3 Generalize and explain strategies for graphing a linear relation in slope–intercept, general or slope–point form.
6.4 Graph, with and without technology, a linear relation given in slope–intercept, general or slope–point form, and explain the strategy used to create the graph.
6.5 Identify equivalent linear relations from a set of linear relations.
6.6 Match a set of linear relations to their graphs.

Determine the equation of a linear relation, given:

a graph
a point and the slope
two points
a point and the equation of a parallel or perpendicular line to solve problems.
[CN, PS, R, V]
7.1 Determine the slope and y-intercept of a given linear relation from its graph, and write the equation in the form y = mx + b.

Slope-y-intercept form

y = mx+ b

m = slope
b = y-intercept

Linked Source - Ron Blond

7.2 Write the equation of a linear relation, given its slope and the coordinates of a point on the line, and explain the reasoning.

Slope–point form

(y – y₁) = m(x – x₁)

m = slope

( x₁, y₁) = one point on the graph

Linked Source - Ron Blond

7.3 Write the equation of a linear relation, given the coordinates of two points on the line, and explain the reasoning.

Slope–point form

(y₂ – y₁) = m(x₂ – x₁)

m = slope
( x₁, y₁) = one point on the graph
( x₂, y₂) = second point on the graph

Substitute coordinates for two points into the slope-point formula. Calculate m.

Use m and one of the points to generate the equation of the linear relation.

(y – y₁) = m(x – x₁) or (y – y₂) = m(x – x₂)

m = slope

( x₁, y₁) = one point on the graph

( x₂, y₂) = second point on the graph

Linked Source - Ron Blond

7.4 Write the equation of a linear relation, given the coordinates of a point on the line and the equation of a parallel or perpendicular line, and explain the reasoning.

Parallel

If two line segments are parallel, the slopes of the two line segments are the same.

Describe Slope

A slope is positive if it rises to the right (as you look at a graph). Remember, if the slope is positive, things are "looking up".
A slope is negative if it falls to the right. Remember, if the slope is negative, things are "looking down".
If the numerical value is high, (whether positive or negative), the slope is steep.
If the numerical value is low, the slope is shallow (more flat).
If the slope is 0, then the line is flat (horizontal).

Perpendicular

If two line segments are perpendicular, the slopes of the two lines are negative reciprocals.

Linear Relation Interactive Activity

Change the slope of a line segment by clicking and dragging on one of the end points. Find examples where the slope of a segment is positive, negative, steep, vertical, shallow and horizontal. The statements on the left will be helpful.

Linked Source - Ron Blond

Perpendicular Line Segments

If two line segments are perpendicular, the slopes of the two lines are negative reciprocals.
Study the lines as you turn one of them. Notice that in each postion, one line is rising and one is falling. This is the reason the slopes are negative reciprocals.
For example if the slope of one segment is 2, the slope of the perpendicular segment is -1/2.
The product of the slopes of two perpendicualr segments is -1. For the previous example:
2 ( -1/2) = -1

Negative Reciprocal Slopes Interactive Activity

Change the slope of the two line segments by clicking and dragging on one of the end points. Study the slopes and product of the two slopes provided in the display area..

Linked Source - Ron Blond

Slope–point form

m₁ = slope of original line.

Parallel

m = m₁
( x₁, y₁) = one point on the graph

(y – y₁) = m(x – x₁)

Perpendicular

( x₁, y₁) = one point on the graph

(y – y₁) = m(x – x₁)

Linked Source - Ron Blond

7.5 Graph linear data generated from a context, and write the equation of the resulting line.
7.6 Solve a problem, using the equation of a linear relation.

Represent a linear function, using function notation.
[CN, ME, V
Select [ Describing Functions ] and/or [ Function Notation ] and/or [ vertical line test ] - will need district login credentials for LearnAlberta

8.1 Express the equation of a linear function in two variables, using function notation.
8.2 Express an equation given in function notation as a linear function in two variables.
8.3 Determine the related range value, given a domain value for a linear function;

e.g., if f(x) = 3x – 2, determine f(–1).

8.4 Determine the related domain value, given a range value for a linear function

e.g., if g(t) = 7 + t, determine t so that g(t) = 15.

8.5 Sketch the graph of a linear function expressed in function notation.

Solve problems that involve systems of linear equations in two variables, graphically and algebraically.
[CN, PS, R, T, V]
[ICT: C6–4.1]
9.1 Model a situation, using a system of linear equations.
9.2 Relate a system of linear equations to the context of a problem.
9.3 Determine and verify the solution of a system of linear equations graphically, with and without technology.

Solve systems of linear equations, in two
variables graphically.

The intersection of the graph of two linear equations is the point(s) of intersection between the two lines.

NOTE: The fastest and easiest method of graphing is using the slope-intercept method (y=mx+b).

Relation 1: y = m₁x + b₁
Relation 2: y = m₂x + b₂

There are 3 types of solutions to systems of linear relations:

If m₁≠ m₂, the lines intersect in one place.

There is one solution - the coordinates of the ordered pair satisfying both relations.

If m₁ = m₂ and b₁ ≠ b₂, the lines are parallel.

There is no solution (intersection).

If m₁ = m₂ and b₁ = b₂, the two relations define the same line (they intersect at all points). The two relatons reduce to the same relation.

There is an infinite number of solutions - all the points on the lines.

Linear Systems Interactive Activity

Focus attention on the y = mx + b form for LINE ONE and LINE TWO.

Manipulate the m and b sliders for each line to see see the effect on the intersection(solution) of the linear system.

Linked Source - Ron Blond

Solving Systems of Linear Equations (Graphing)

Alberta Education Terms of Us

9.4 Explain the meaning of the point of intersection of a system of linear equations.
9.5 Determine and verify the solution of a system of linear equations algebraically.

substitution

simple elimination

one/two step elimination

3 variable - Matrix

9.6 Explain, using examples, why a system of equations may have no solution, one solution or an infinite number of solutions.

The intersection of the graph of two linear equations is the point(s) of intersection between the two lines.

NOTE: The fastest and easiest method of graphing is using the slope-intercept method (y=mx+b).

Relation 1: y = m₁x + b₁
Relation 2: y = m₂x + b₂

There are 3 types of solutions to systems of linear relations:

If m₁≠ m₂, the lines intersect in one place.

There is one solution - the coordinates of the ordered pair satisfying both relations.

If m₁ = m₂ and b₁ ≠ b₂, the lines are parallel.

There is no solution (intersection).

If m₁ = m₂ and b₁ = b₂, the two relations define the same line (they intersect at all points). The two relatons reduce to the same relation.

There is an infinite number of solutions - all the points on the lines.

Linear Systems Interactive Activity

Focus attention on the y = mx + b form for LINE ONE and LINE TWO.

Manipulate the m and b sliders for each line to see see the effect on the intersection(solution) of the linear system.

Linked Source - Ron Blond

9.7 Explain a strategy to solve a system of linear equations.
9.8 Solve a problem that involves a system of linear equations.

March, 2008 http://www.education.alberta.ca/media/655889/math10to12.pdf

2008 Program of Studies with Achievement Indicators: http://education.alberta.ca/media/823110/math10to12_ind.pdf

Authorized Resources: http://www.education.alberta.ca/teachers/program/math/educator/resources.aspx