Slope-Intercept Form

Topics for Today:

One of the most recognizable forms of a line is the slope-intercept form.  This line form is very useful because it's easy to visualize the actual line simply by looking at the equation.  From slope-intercept form, you can tell if the slope is positive or negative, and if the slope is steep or shallow, and also it demonstrates where the line crosses the y-axis (this is the y-intercept).

We talked about what an intercept is (this word sounds an awful lot like intersect!).

I reminded students of our work on solving literal equations - this skill will be especially helpful for our unit on linear equations, as we'll be looking at three different forms for a linear equation.  To put a line in slope-intercept form, simply solve for the variable "y".

Slope intercept form looks like this:  y=mx + b

• m is the slope
• b is the y-intercept 

Vocabulary: linear equation, y-intercept, slope-intercept form

Sections Covered in Textbook:

6-2: Slope-Intercept Form (pages 291-296)

Resources & Tutorials:

1) What is a linear equation?
2) What is the y-intercept?
3) What is the slope-intercept form of a line?

Rate of Change and Slope

Topics for Today:

We will continue our discussion about functions as we explore linear functions (lines).  ALL LINES (with the exception of vertical lines) are functions.  This unit will cover many different aspects of line, beginning with rate of change, otherwise known as slope.  We associate slope with the "steepness" of a line.  Slopes can be positive, negative, zero, or undefined.

Slope is a 2-dimensional concept.  We will see how fast something rises (goes up) compared to how fast it travels in a horizontal direction.  Slope is defined as the change in the y-coordinate divided by the change in the x-coordinate.  To calculate slope, you need any two points on a line.  It does not matter where you start as long as you start in the same place for each component.

Vocabulary: rate of change, slope

Sections Covered in Textbook:

6-1: Rate of Change and Slope (pages 282-289)

Resources & Tutorials:

1) What does the slope of a line mean?
2) How do you find the slope of a line from two points?
3) How do you find the slope of a line from a graph?