MPM 1DI
EXAM and EQAO REVIEW
Day 2 ­ Chapter 5 REVIEW
Modelling with Graphs (chapter 5 in
text)
Ø Direct/Partial Variation
J Direct Variation: y = mx
*initial value (y-int) is 0
J Partial Variation: y = mx + b
*initial value (y-int) is NOT 0
Ø First Difference Tables
Ø Slope
J constant of variation
J rate of change or unit rate
J
J
J
Example 1: Identify each of the following as direct
variation, partial variation or neither
Example 2:
Correct the error in the table to make it a linear
relation.
X
Y
2
­5
­1
­2
­4
0
­7
4
­10
7
Example 3:
Given the following set of line segments.
a) Name the line
segment that
has the
steepest
negative slope.
b) What is the
slope of CD?
IJ?
GH?
EF?
Example 4:
What is the slope of the line segment joining the
points P(0, 7) and B(-2, -4)?
Example 7:
The pronghorn antelope is the fastest North American
mammal. It can run 200m in about 7.5s. What is the
average speed of the antelope?
Example 8:
The distance-time graph shows Tracy‛s motion in
front of a motion sensor.
a) Identify the d ­ intercept and explain what it means.
b) Identify the t ­ intercept
and explain what it means.
Example 9:
The cost of a taxi ride is $5.00 plus $0.75 for every
km travelled.
a) Graph this relation
b) Identify the slope
and vertical intercept
of the line. What do
they represent?
c) Is this direct or partial
vartiation? Explain.
d) Write an equation relating the cost and distance
travelled.
MPM 1DI
EXAM and EQAO REVIEW
Chapter 6 REVIEW
Analyzing Linear Relations Ø Equations of Lines in slope/y-intercept form y=mx + b,
where m is the slope, b is the y intercept (where
the graph crosses the y-axis, the point where x is
zero).
Ø Equations of Lines in standard form Ax + By + C = 0
leading coefficient must be positive
no fractions
no decimals
= 0 on right side
Ø Horizontal / Vertical Lines
Ø Graphing Using Intercepts
Ø Parallel Lines (slopes are equal)
Ø Perpendicular Lines (slopes are negative reciprocals)
Ø Finding Equation of a Line given a point and a slope
Ø Finding Equation of a Line given two points
Ø Linear Systems (finding point of intersection of two
lines)
Example 1: Graph the line y=-3x-2 using the slope and
y-intercept
Example 2: Write the equation 2x - 4y =10 in slope/y-intercept
form.
Example 3: The equations of four lines are given:
x=-3
y=-x+3
y=5
y=2x-4
Which of these lines represents:
a. a vertical line
b. a horizontal line
c. a line that slopes upward to the right
d. a line that slopes downward to the right.
Example 4:
Graph 2x - 4y = 10 using intercepts.
Example 5:
Find the point of intersection of the two lines by graphing.
Check your answer.
y=-3x+1
y=x+5
Example 6:
Determine the equation of the lines that have the following
characteristics (put your answers in slope y-intercept form):
(a) y-intercept = 3 and perpendicular to a line with slope ½
(b) parallel to the line x=2 and passing through the point (5,7)
(c) through (-4,-1) with slope ½
(d) with an x-intercept of 6 and y-intercept of 4
(e) through the points (-1,7) and (-5,3)