Point-Slope Form

Topics for Today:

Today we discussed the last line form, point-slope form, through a PowerPoint presentation (link below).  

The three different forms of a linear equation are all useful for different reasons.  Each one has a pattern to follow.  Once the patterns are mastered, linear graphing becomes much easier.  

Vocabulary: point-slope form

Sections Covered in Textbook:

6-4: Point-Slope Form and Writing Linear Equations (pages 304-309)

Resources & Tutorials:

1) What is the point-slope form of a linear equation?

2) How do you write an equation of a line in point-slope form if you have the slope and one point?

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3) Exploring Point-Slope Form (PowerPoint)

Standard Form

Topics for Today:

Our discussion about linear equations continued today.  We have already explored slope and slope-intercept form of a line.  Today, we looked at a different form - standard form.  The standard form of a line is defined as a linear equation such that

Ax + By = C

A, B, and C must all be integers.

A must be positive.

Although it's easy to visualize a line that is in slope-intercept form (the form we worked with yesterday), it's very easy to find both the x- and y-intercepts when a line is in standard form.  These intercepts are where the line crosses the x- and y-axes, when one of our coordinates is zero.  Solving the equation when substituting a zero for a value is a quick process, because multiplying by zero removes the variable from the equation.  Once we find our intercepts, it's very easy to graph our equation.

Standard form can be nice for students who are not fond of working with fractions, and we'll be using standard form when we move to solving systems of equations in the next chapter.  In addition, many of the other graphs that students will see in later mathematics classes are written in standard form with the variables all on one side of the equation.  Comfort with standard form will help students cope when they are introduced to more complicated equations.

Vocabulary: standard form of a line, x-intercept

Sections Covered in Textbook:

6-3: Standard Form (pages 298-302)

Resources & Tutorials:

1) What is the standard form of a linear equation?
2) How do you use x- and y-intercepts to graph a line in standard form?

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?