Xc ngwenya 201007180

Mathematics : grade11

Functions : linear equationsX.C NGWENYA

201007180

Lesson outcome Lesson outcome

Identify linear equations and functions.

Write linear equations in standard form and graph them.

You will learn to calculate the

y-intercept x-intercept

INTRODUCTION

• A linear equation is an algebraic equation in which each term is either a constant or the product of a constant and (the first power of) a single variable.

• Linear equations can have one or more variables. Linear equations occur with great regularity in applied mathematics. Linear equations do not include exponents.

• A common form of a linear equation in the two variables x and y is y= mx + c

y

x

6

0

4-2-2

2

6

-2 6

0

-2

6

2

4

4 yx

Spounge has 4 hours after dinner to study and dohomework. He has brought home algebra 2and chemistry.

If he spends x hours on algebra and y hours on chemistry, a portion of the graphof the equation x + y = 4 can be used to relate how much time she spends on each.

An equation such as x + y = 4 is called a linear equation.

Linear Equations Linear Equations

A linear equation has no operations other than:

________, ___________, and ____________________________________.addition subtraction multiplication of a variable by a constant

The variables may not be multiplied together or appear in a ____________.

A linear equation does not contain variables with exponents other than __.1

denominator

The graph of a linear equation is always a ____.line

Linear Equations Not Linear Equations

735 yx

9x

1536 ts

xy21

847 2 ba

5 xy

1 xyx

xy1


A linear function is a function whose ordered pairs satisfy a linear equation.

Any linear function can be written in the form f(x) = mx + b, where m and bare real numbers.

State whether each function is a linear function. Explain.

a) f(x) = 10 – 5x





a) f(x) = 10 – 5x Yes!





a) f(x) = 10 – 5x Yes!

It can be written as f(x) = – 5x + 10m = – 5, b = 10

b) g(x) = x4 – 5





a) f(x) = 10 – 5x Yes!


b) g(x) = x4 – 5 No!





a) f(x) = 10 – 5x Yes!


b) g(x) = x4 – 5 No!

x has an exponent other than 1.





a) f(x) = 10 – 5x Yes!


b) g(x) = x4 – 5 No!


c) h(x, y) = 2xy





a) f(x) = 10 – 5x Yes!


b) g(x) = x4 – 5 No!


c) h(x, y) = 2xy No!





a) f(x) = 10 – 5x Yes!


b) g(x) = x4 – 5 No!


c) h(x, y) = 2xy No!

Two variables are multiplied together.


Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.

y

x

Example Example

1535 yx


y

x

The x-intercept is the value of x when y = 0.


1535 yx

15)0(35 x


y

x



1535 yx

15)0(35 x

155 x


y

x


(3, 0)


1535 yx

15)0(35 x

155 x

3x


y

x


(3, 0)


1535 yx

15)0(35 x

155 x

3x

The y-intercept is the value of y when x = 0.

153)0(5 y


y

x

The x-intercept is the value of x when y = 0.(0, 5)

(3, 0)


1535 yx

15)0(35 x

155 x

3x


153)0(5 y

153 y

5y


y

x


(3, 0)


1535 yx

15)0(35 x

155 x

3x


153)0(5 y

153 y


y

x


(3, 0)


1535 yx

15)0(35 x

155 x

3x


153)0(5 y

153 y

5y

(0, 5)


y

x

The x-intercept is the value of x when y = 0.(0, 5)

(3, 0)

1535 yx

15)0(35 x

155 x

3x


153)0(5 y

153 y

5y

homeworkhomework

Evaluate each function rule for x = –5.

1. y = x – 7 2. y = 7 – x

3. y = 2x + 5 4. y = – x + 3

Draw the graph of y= 5x + 4

Find x and y intercepts of f(X)

references references

BibliographyFant, R. (2005). linear equations., (pp. 15-17).

Glencoe. (2005). algebra2.

Ridgell. (n.d.). rate of change and slope., (p. chapter 6).

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