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You Tube video of Y=mx + b
Friday, February 21, 2014
Wednesday, February 19, 2014
Tuesday, February 18, 2014
Algebra Honors ( Periods 6 & 7)
Points, Lines, and Their Graphs 8-2
We reviewed graphing or plotting an ordered pair as a point on a coordinate plane.
Horizontal axis is the x-axis
vertical axis is the y-axis
origin is at (0,0)
an ordered pair (3,2) lists the coordinates of a point. In this instance we called the Point A
3 is the x-coordinate also know as the abscissa of A
2 is the y-coordinate also known as the ordinate of A
the x- and y-axes are also called coordinate axes and the number plane is often called the coordinate plane. The coordinate axes separate a coordinate plane into four quadrants identified by Roman Numerals. See page 354 for details.
Points on the coordinate axes are NOT considered to be in any quadrant.
The graph of an equation in two variables consists of all the points that are the graphs of the solutions of the equations.
x + 2y = 6 has the following ordered pairs:
(0,3)
(2,2)
(4,1)
(6,0)
There are infinite number of solutions-- such as
(-2,4)
(1, 2.5)
The graph of all the solutions lie on the straight line that is drawn when the points are connected.
x + 2y = 6 is a linear equation because its graph is a line.
All linear equations in the variables x and y can be written in the form
ax + by = c
or
Ax + By = C
where a, b, and c are real numbers with a and b not both zero. If a, b, and c are integers, then the equation is said to be in standard form. We determined that A must be a whole number. A greater than or equal to 0.
2x -5y = 7 and 4x + 9y = 0 and y = 3 are examples of linear equations in standard form
(1/2)x + 4y = 12 is not
y = 3x -1 is not
neither is x2y + 3y = 4
nor xy = 6
Although you only need two points to determine a line, I suggest you plot 3-- whenever possible to guard against mistakes.
The easiest solutions to find are those where the line crosses
the x-axis ( y = 0) and
the y-axis ( x = 0)
We reviewed graphing or plotting an ordered pair as a point on a coordinate plane.
Horizontal axis is the x-axis
vertical axis is the y-axis
origin is at (0,0)
an ordered pair (3,2) lists the coordinates of a point. In this instance we called the Point A
3 is the x-coordinate also know as the abscissa of A
2 is the y-coordinate also known as the ordinate of A
the x- and y-axes are also called coordinate axes and the number plane is often called the coordinate plane. The coordinate axes separate a coordinate plane into four quadrants identified by Roman Numerals. See page 354 for details.
Points on the coordinate axes are NOT considered to be in any quadrant.
The graph of an equation in two variables consists of all the points that are the graphs of the solutions of the equations.
x + 2y = 6 has the following ordered pairs:
(0,3)
(2,2)
(4,1)
(6,0)
There are infinite number of solutions-- such as
(-2,4)
(1, 2.5)
The graph of all the solutions lie on the straight line that is drawn when the points are connected.
x + 2y = 6 is a linear equation because its graph is a line.
All linear equations in the variables x and y can be written in the form
ax + by = c
or
Ax + By = C
where a, b, and c are real numbers with a and b not both zero. If a, b, and c are integers, then the equation is said to be in standard form. We determined that A must be a whole number. A greater than or equal to 0.
2x -5y = 7 and 4x + 9y = 0 and y = 3 are examples of linear equations in standard form
(1/2)x + 4y = 12 is not
y = 3x -1 is not
neither is x2y + 3y = 4
nor xy = 6
Although you only need two points to determine a line, I suggest you plot 3-- whenever possible to guard against mistakes.
The easiest solutions to find are those where the line crosses
the x-axis ( y = 0) and
the y-axis ( x = 0)
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