Algebra Honors ( Periods 5 & 6)

The Slope-Intercept Form of a Linear Equation 8-4

For every real number, the graph of the equation y = mx is the line that has slope m and asses thrugh the origin.

For all real numbers m and b, the graph of the equation

y = mx + b

is the line whose slop is m and whose y-intercept is b.

This is called the slope intercept form of an equation of a line.

Find the slope and y-intercept of

We know m = 3/5 and b = 2

so the slope is 3/5and the y-intercept is 2

 Using only the slope and y-intercept to graph

The slope = -3/4 and the y-intercept is 6

Since the y-intercept is 6 you plot (0, 6)

Since the slop is -3/4 move 3 units down and 4 units to the right to locate a second point.

Draw the line between the two points and write the equation of the line directly above the line.

(Check our textbook)

Use only the slope and y-intercept to graph

2x – 5y = 10

Solve for y to transform the equation into the form y = mx + b

2x -5y = 10

-5y = -2x + 10

the slope is 2/5 and the y intercept is -2

Since the y intercept is -2, plot ( 0, -2)

Since the slope is 2/5 move 2 units up and 5 units to the right to locate the second point. Draw the line through the two points and write the equation directly above the line.

SEE TEXBOOK for the accurate graph

Lines in the same plane that do not intersect are PARALLEL.

Different lines with the same slope are parallel

Parallel lines that are not vertical have the same slope.

Show that the lines whose equations are 2x + y = 8 and y = -2x + 6 are parallel

write each equation in slope-intercept form

2x + y = 8 becomes y = -2x + 8

and the 2^nd one is y - -2x + 6

Slope of both is -2

Since both lines have the same slope AND different y–intercepts, they are parallel.

Perpendicular Lines

Any two lines that intersect to form right angles are perpendicular. 

In a plane, two lines that are not horizontal or vertical are perpendicular if and only if the product of their slopes is -1.

In a plane vertical lines and horizontal lines are perpendicular.

Show that the graphs of the following lines  are perpendicular

Write 6y + 8x = 7 in slope intercept form

The slope is -4/3

The slope of the first equation is ¾

(3/4)(-4/3) = -1

Therefore the lines are perpendicular

What about y = x + 6

and y = -x +4

they are perpendicular because (1)(-1) = -1

Math 6H ( Period 3)

The Tangram Story
(One of the activities we did while students were at Astro Camp)

Once upon a time, long, long ago, in a faraway magical land lived a little boy named Tan. The emperor of the land had entrusted Tan with a very special task. The emperor had given Tan a magical square tile and asked him to deliver it to one of the emperor’s subjects who lived in the countryside. Tan was instructed to go directly to the subject’s house and not stop along the way. But, along the way, Tan encountered a group of his friends playing along the river. Tan thought he would stop for just a few minutes to rest and play … when alas; the tile flew out of his pocket and broke into seven pieces. Tan and his friends were so upset that they tried for days to put the tile back together again. They were able to form many beautiful designs of birds and animals and flowers but never the square tile. His designs have been handed down form generation to generation for over 3000 years and are known as Tangram puzzles.
If you would like to enjoy creating some of these puzzles or are interested in how to create your own tile, come in before or after school.

Math 6A (Periods 2 & 4)

The Tangram Story
(One of the activities we did while students were at Astro Camp)

Once upon a time, long, long ago, in a faraway magical land lived a little boy named Tan. The emperor of the land had entrusted Tan with a very special task. The emperor had given Tan a magical square tile and asked him to deliver it to one of the emperor’s subjects who lived in the countryside. Tan was instructed to go directly to the subject’s house and not stop along the way. But, along the way, Tan encountered a group of his friends playing along the river. Tan thought he would stop for just a few minutes to rest and play … when alas; the tile flew out of his pocket and broke into seven pieces. Tan and his friends were so upset that they tried for days to put the tile back together again. They were able to form many beautiful designs of birds and animals and flowers but never the square tile. His designs have been handed down form generation to generation for over 3000 years and are known as Tangram puzzles.
If you would like to enjoy creating some of these puzzles or are interested in how to create your own tile, come in before or after school.

Algebra Honors ( Periods 5 & 6)

Check this out & have fun learning the words to y = mx +b

Algebra Honors (periods 5 & 6)

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 poins 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 noth both zero. If a, b, and c are integers, then the equation is said to be in standard form.

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)