This document describes linear equations and their graphical representations. It explains that equations of the form y=mx represent proportional relationships with slope m passing through the origin, while equations of the form y=mx+b with b not equal to 0 represent non-proportional relationships with slope m passing through the point (0,b). It also notes that vertical lines have undefined slope since the x-values do not change as y changes. The document provides examples of linear graphs and asks the reader to determine if they represent proportional or non-proportional relationships and write the corresponding equations.

1. PRIMETIME : 11/16/2023

2. Activity 4
Describing Linear Equations
You know that the equation y = mx represents a proportional
relationship. The equation represents every point (x, y) on
the graph of a line with slope m that passes through the
origin (0, 0).
An equation of the form y = mx + b, where b is not equal to
zero, represents a non-proportional relationship. This
equation represents every point (x, y) on the graph of a line
with slope m that passes through the point (0, b).

3. Activity 4
In a vertical line, there is no change in the x-values as the y-
values change. Therefore, the slope is undefined. A vertical line
has an undefined steepness.
1. Consider each graph shown.
• Determine whether the graph represents a proportional or
non-proportional relationship.
• Write an equation in the form y = mx or y = mx + b to
represent the relationship between the independent and
dependent quantities.

4. Activity 4
a) b)

5. Activity 4
c) d)

6. e) f)

7. HOMEWORK
m = -5
m = 1/3
m = - 1/5 undefined