Discuss the Ideas
1. When a real-world situation can be modelled by a linear function, what do
the slope and vertical intercept usually represent?
The slope represents the rate of change; that is how one quantity changes
with respect to another quantity.
The vertical intercept usually represents the initial value in a context; for
example, the initial distance from a destination, or the volume of fuel in a full
tank.
2. When you are given the graph of a linear function, how can you determine
an equation that represents that function?
You need to determine the slope of the line and its y-intercept. You substitute
y = mx + b
the values in the equation form:
.
3. When you are given an equation of a linear function in slope-y-intercept
form, how can you quickly sketch the graph?
When an equation of a linear function in slope-intercept form is given, you
would use the value of the y-intercept and locate it on the graph, and then
continue to find the next point by apply the rise and run values.