Pearson
Foundations and Pre-calculus Mathematics 10
Lesson 6.3
Chapter 6
Linear Functions
Math Lab:
Assess Your Understanding (page 356)
Investigating Graphs of Linear Functions
1. Each line has an equation of the form y = mx + b, where m is the slope and b is the
y-intercept.
1
1
, then the equation of each line has the form y = x + b
2
2
From the top of the screen to the bottom, the equations are:
1
1
1
1
1
y = x + 4, y = x + 2, y = x – 1, y = x – 2, y = x – 3
2
2
2
2
2
a) Since the slope of each line is
1
b) Since the slope of each line is  , then the equation of each line has the form
3
1
y=  x+b
3
From the top of the screen to the bottom, the equations are:
1
1
1
1
1
y =  x + 4, y =  x + 3, y =  x + 1, y =  x – 2, y =  x – 3
3
3
3
3
3
2. The graph of a function with an equation of the form y = mx + b has a slope of m and a yintercept of b. To graph the function, I would mark a point at the y-intercept, then use the
slope to identify the rise and run. From the y-intercept, I would move vertically a number of
squares equal to the rise, then horizontally a number of squares equal to the run, then mark
another point. When I draw a line through the points, I have drawn a graph of the function.
3. The graph of the linear function with equation y = –3x + 6 has a y-intercept of 6 and a slope
of –3. From 6 on the y-axis, I move 3 squares down, then 1 square right and mark a point. I
draw a line through this point and the point at the y-intercept. This line is the graph of the
function.
4. a) Predictions may vary. For example:
When m is positive, the graphs go up to the right. As m increases, the graphs get steeper.
When m is negative, the graphs go down to the right. As m decreases, the graphs get
steeper.
b)
i) The graph of y = x – 1 has slope 1 and y-intercept –1. From –1 on the y-axis, I move
1 square up, then 1 square right and mark a point. I draw a line through this point and
the point at the y-intercept.
Lesson 6.3
Copyright  2011 Pearson Canada Inc.
1
Pearson
Foundations and Pre-calculus Mathematics 10
Chapter 6
Linear Functions
ii) The graph of y = 2x – 1 has slope 2 and y-intercept –1. From –1 on the y-axis, I move
2 squares up, then 1 square right and mark a point. I draw a line through this point
and the point at the y-intercept.
iii) The graph of y = –3x – 1 has slope –3 and y-intercept –1. From –1 on the y-axis, I
move 3 squares down, then 1 square right and mark a point. I draw a line through this
point and the point at the y-intercept.
iv) The graph of y = –2x – 1 has slope –2 and y-intercept –1. From –1 on the y-axis, I
move 2 squares down, then 1 square right and mark a point. I draw a line through this
point and the point at the y-intercept.
The graphs show that my predictions in part a were correct.
5. a) Predictions may vary. For example:
The graph moves up if b is increasing and the graph moves down if b is decreasing.
b)
i) The graph of y = x – 3 has slope 1 and y-intercept –3. From –3 on the y-axis, I move
1 square up, then 1 square right and mark a point. I draw a line through this point and
the point at the y-intercept.
ii) The graph of y = x – 2 has slope 1 and y-intercept –2. From –2 on the y-axis, I move
1 square up, then 1 square right and mark a point. I draw a line through this point and
the point at the y-intercept.
iii) The graph of y = x has slope 1 and y-intercept 0. From the origin, I move 1 square up,
then 1 square right and mark a point. I draw a line through this point and the point at
the y-intercept.
iv) The graph of y = x + 3 has slope 1 and y-intercept 3. From 3 on the y-axis, I move 1
square up, then 1 square right and mark a point. I draw a line through this point and
the point at the y-intercept.
The graphs show that my prediction in part a was correct.
6. I used the same strategy as in question 3.
Lesson 6.3
Copyright  2011 Pearson Canada Inc.
2
Pearson
Foundations and Pre-calculus Mathematics 10
Chapter 6
Linear Functions
a) The graph of y = 3x + 5 has slope 3 and y-intercept 5. From 5 on the y-axis, I move 3
squares up, then 1 square right and mark a point. I draw a line through this point and the
point at the y-intercept.
b) The graph of y = –3x + 5 has slope –3 and y-intercept 5. From 5 on the y-axis, I move 3
squares down, then 1 square right and mark a point. I draw a line through this point and
the point at the y- intercept.
c) The graph of y = 3x – 5 has slope 3 and y-intercept –5. From –5 on the y-axis, I move 3
squares up, then 1 square right and mark a point. I draw a line through this point and the
point at the y-intercept.
d) The graph of y = –3x – 5 has slope –3 and y-intercept –5. From –5 on the y-axis, I move 3
squares down, then 1 square right and mark a point. I draw a line through this point and
the point at the y-intercept.
7. a) The graph of C = 550 + 15n has a C-intercept of 550 and a slope of 15. Since n is a whole
number, the graph is a set of points. From 550 on the C-axis, I move 15 up and 1 right.
Since it is difficult to move 15 up when the scale is 1 square represents $100, I move 150
up and 10 right, then mark a point. From this point, I move 150 up and 10 right, then
mark another point. I use a straightedge to mark more points along this line at different
values of n.
Lesson 6.3
Copyright  2011 Pearson Canada Inc.
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Pearson
Foundations and Pre-calculus Mathematics 10
Chapter 6
Linear Functions
b) m represents the slope or rate of change; that is, $15 per person. b represents the initial
cost of $550 to rent the hall. After this has been paid, each additional person costs $15.
Lesson 6.3
Copyright  2011 Pearson Canada Inc.
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Pearson
Foundations and Pre-calculus Mathematics 10
Lesson 6.3
Copyright  2011 Pearson Canada Inc.
Chapter 6
Linear Functions
5