2. Review
If y is proportional to x ,
then
When express y in terms of x
, y = ?
If y is inversely proportional to x ,
then
When express y in terms of x
, y = ?
4. Linear Functions
What is a linear function?
It’s a function that can be represented as
and are constants and
How do we determine whether a function is linear or nonlinear?
5. o A linear equation in two variables, x and y, is an equation that can be
written in the form , where a and b are constants (just numbers).
o Likewise, a linear function is a function whose graph is a non-vertical line.
o A linear function has a constant rate of change and can be represented by a
linear equation in two variables.
o A nonlinear function does not have a constant rate of change and its graph is
not a line.
6. o If you let be the total cost of a 40-yen bottle filled with grams of a drug
costing 8-yen per gram, then
(Total cost) = (Cost of drug) + (Cost of bottle),
o It takes seconds to run 400m at a speed of metres per second
Time =
Examples
7. o In the rectangle on the right, Point P moves from B to C on side BC. Letting
cm be the length of segment BP and cm2
be the area of the DPC
1. in terms of
2. Is a linear function of ?
3. Find value for y when = 0 and value of when = 12
4. Domain of x and domain of y (when point P is at vertices B and C)
Examples
8. Does the table represent a linear or nonlinear function?
A linear function has a constant rate of change
As x increases by 3, y decreases by 6.
The rate of change is constant for both
x and y.
The function is linear.
x 3 6 9 12
y 36 30 24 18
+3 +3 +3
-6 -6 -6
9. Does the table represent a linear or nonlinear function?
A linear function has a constant rate of change
As x increases by 2, y increases by
different amounts.
The rate of change is not constant for
both x and y.
The function is nonlinear.
x 1 3 5 7
y 2 9 20 35
+2 +2 +2
+7 +11 +15
10. o When the x value goes from 2 to 8 in the linear function , find increase in ,
increase in and the rate of change,
Increase in is 8 – 2 = 6
Increase in
Rate of change is
Examples
11. Does the graph represent a linear or nonlinear function? Explain.
The function is linear.
Because the graph is a
line.
The function is nonlinear.
Because the graph is not
a line.
12. Which of the following equations represent linear functions? Explain.
A linear function can be written in the form , where m and b are constants (just
numbers).
You cannot rewrite the equations , , , and in the form .
So these equations cannot represent linear functions.
You can rewrite the equation as
You can rewrite the equation as
So these equations represent linear functions.
, , , , , and
13. Does the equation represent a linear or nonlinear function? Explain.
A linear function can be written in the form .
You can rewrite the
equation as
Equation represents a
linear function.
You can rewrite the
equation as
Equation represents a
linear function.
You cannot rewrite the
equation as
Equation is a nonlinear
function.
14. Graphs of proportion & linear functions
The graph of a linear function is a straight line formed by translating the graph
of by the amount in the +ve direction along the y-axis.
𝑦 =2 𝑥+ 3
15. For the linear function , complete the table.
Substitute each x and y value in the eqn using values.
𝑦
=
2
𝑥
+
3
3
16. The graph of the linear function is a st line with a slope of a and b.
The slope is equal to
Y intercept is equal to
the constant -3.
Editor's Notes
#3:y=ax is a straight line passing through the origin and point (1, -2)
y=6/x is a hyperbola
#4:Y = ax is proportional. That is also linear function when This is a linear relationship and function.
#7:To answer these questions, let's define the situation clearly.
We have a rectangle where Point P moves along side BC from B to C.
BP = x cm represents the position of P along BC.
yyy is the area of △DPC\triangle DPC△DPC (a right triangle).
Area=1/2×base×height
