Transcript 4.5 Graphing Linear Equations

4.5 Graphing Linear Equations
• A linear equation can be written in the
form Ax + By = C.
• This is called the standard form of a
linear equation.
• A ≥ 0, A and B are not both zero, and A, B,
and C are integers whose greatest
common factor is 1.
Identify Linear Equations
•
Determine whether each equation is a linear
equation. If so, write the equation in standard
form.
a. y = 5 – 2x
y + 2x = 5 – 2x + 2x
2x + y = 5
The equation is now in standard form where
A = 2, B = 1, and C = 5. This is a linear
equation.
Identify Linear Equations
•
Determine whether each equation is a linear
equation. If so, write the equation in standard
form.
b. 2xy – 5y = 6
Since the term 2xy has two variables, the
equation cannot be written in the form
Ax + By = C. Therefore, this is not a linear
equation.
•
Identify Linear Equations
Determine whether each equation is a linear
equation. If so, write the equation in standard
form.
c. 3x + 9y = 15
Since the GCF of 3, 9, and 15 is not 1, the
equation is not written in standard form.
Divide each side by the GCF.
3x + 9y = 15
3(x + 3y) = 15
x + 3y = 5
The equation is now in standard form where
A = 1, B = 3, and C = 5.
•
Identify Linear Equations
Determine whether each equation is a linear
equation. If so, write the equation in standard
form.
d. 1/3 y = -1
To write the equation with integer coefficients,
multiply each term by 3.
1/3 y = -1
3(1 /3 ) y = 3(-1)
y = -3
The equation y = -3 can be written as 0x + y = -3.
Therefore, it is a linear equation in standard
form where A = 0, B = 1, and C = -3.
Graph Linear Equations
• The graph of a linear equation is a line.
• The line represents all the solutions of the
linear equation.
• Also, every ordered pair on this line
satisfies the equation.
Graph by Making a Table
• Graph x + 2y = 6.
• In order to find values for y more easily, solve
the equation for y.
x + 2y = 6
x + 2y – x = 6 – x
2y = 6 – x
y=3–½x
Graph by Making a Table
Intercepts
• Since two points determine a line, a simple
method of graphing a linear equation is to
find the points where the graph crosses
the x-axis and the y-axis.
• The x-coordinate of the point at which it
crosses the x-axis is the x-intercept, and
the y-coordinate of the point at which the
graph crosses the y-axis is called the yintercept.
Graph Using Intercepts
• Determine the x-intercept and y-intercept
of 3x + 2y = 9. Then graph the equation.
• To find the x-intercept, let y = 0.
3x + 2y = 9
3x + 2(0) = 9
3x = 9
x=3
Graph Using Intercepts
• Determine the x-intercept and y-intercept
of 3x + 2y = 9. Then graph the equation.
• To find the y-intercept, let x = 0.
3x + 2y = 9
3(0) + 2y = 9
2y = 9
y = 4.5
Graph Using Intercepts
• The x-intercept is 3, so the graph intersects the x-axis
at (3 , 0). The y-intercept is 4.5, so the graph
intersects the y-axis is (0 , 4.5). Plot these points.
Then draw a line that connects them.