10.3 Slopes of Linear Graphs

1. Slope: the measure of the steepness of a straight line.

The slope of a line is the measure of the ratio of vertical rise and horizontal run.

The slope of a line = Rise/Run = Vertical change/Horizontal change

Positive slope, negative slope, special slopes for horizontal line and vertical line

2. The slope for any line with two points on the line A(x1, y1) and B(x2, y2)

The slope of a line = Rise/Run = (y2 – y1)/(x2 – x1)

Lots of examples in class.

HW:

• Handout
  • 2 pages
• Workbook:
  • page 11: 9, 10;
  • page 12: 11;
  • page 13: 17

10.2 Linear Graphs

1. General Form

The graph of an equation of the form y = mx + b is a straight line, where b and m are constant.

The graph of an equation that is a straight line is called a linear graph.

2. Special linear graph:

• y = c   — a horizontal straight line that is parallel to the x-axis
• x = a   — a vertical straight line which is parallel to the y-axis

 3. How to draw the graph of y = mx + b

• y = – (1/3)x + 2
• How to create a graph of the linear equation y = 2x + 7

• How to create a graph of the linear equation 5x + 2y = 20

4. Does a point A (x, y) lie on the graph?

5. Homework:

• Handout: 2 pages
• Workbook: page 10. #4, 5, 6, 7, 8

Chapter 10 Coordinates and Linear Graphs

10.1 Cartesian Coordinate System

1. Terminologies: x-axis, y-axis, coordinate axes, origin, first, second, third, and fourth quadrants. The coordinate plane, Cartesian plane, or x-y plane. 

The position of any point, say P, on the plane can be described by an ordered pair (a, b) of real numbers. We obtain the value of a when the vertical line through P intersects the x-axis and the value of b when the horizontal line through P intercepts the y-axis. We call a the x-coordinate and b the y-coordinate of P. We say that P has coordinates (a, b) and refer the point P as P(a, b). Hence, we can locate a point in a plane if we know its x- and y- coordinates.

2. Lots of exercise of stating the coordinates of points in a diagram, and plotting points with coordinates on a coordinate plane.

3. Home Work

• Handout: 2 pages
• Workbook: 

                     page 9: 1, 2

                     page 10: 3