xc ngwenya 201007180
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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
Linear Equations Linear Equations
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
Linear Equations Linear Equations
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 Yes!
Linear Equations Linear Equations
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 Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5
Linear Equations Linear Equations
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 Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
Linear Equations Linear Equations
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 Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
Linear Equations Linear Equations
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 Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy
Linear Equations Linear Equations
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 Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy No!
Linear Equations Linear Equations
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 Yes!
It can be written as f(x) = – 5x + 10m = – 5, b = 10
b) g(x) = x4 – 5 No!
x has an exponent other than 1.
c) h(x, y) = 2xy No!
Two variables are multiplied together.
Linear Equations Linear Equations
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
Example Example
1535 yx
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
Linear Equations Linear Equations
1535 yx
15)0(35 x
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.(0, 5)
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
5y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.(0, 5)
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
5y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
y
x
The x-intercept is the value of x when y = 0.
(3, 0)
Linear Equations Linear Equations
1535 yx
15)0(35 x
155 x
3x
The y-intercept is the value of y when x = 0.
153)0(5 y
153 y
5y
(0, 5)
Find the x-intercept and the y-intercept of the graph of the equation.Then graph the equation.
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
The y-intercept is the value of y when x = 0.
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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