FPC Math
10 Linear Equations in "Slope- y-intercept" form.
Yesterday we learned how to find the line equation in slope-point form.
Today we shall look at how to find the line equation in another form called
"slope-y-intercept" form.
Before we start the process, let us test our observation skill and see how well
we make the connection of the line equations and its graphs.
Look at the following graphs: their equations are given in slope-y-intercept form .
Can you see the connection?
Math 10 Unit 6 Linear Functions
Name:______Key_______
Lesson Notes: 6.3: Slope-y-intercept Form of the Equation for a Linear Function.
LESSON FOCUS: Relate the graph of a linear function to its equation in
slope-y-intercept form.
Make Connections
This graph shows a cyclist’s journey where the
distance is measured from her home.
What does the vertical intercept represent?
y-intercept at 10 km is the place where the cyclist
started her journey and it is 10 km from her home.
What does the slope of the line represent?
The slope represents her cycling speed of her journey.
In Chapter 5, we described a linear function in different ways. The linear
function below represents the cost of a car rental.
An equation of the function is:
C = 0.20d + 60
The number, 0.20, is the rate of change, or
the slope of the graph. This is the cost in
$/km driven. The number, 60, is the vertical
intercept of the graph. This is the cost in dollars
that is independent of the distance driven – the
initial cost (fixed cost) for renting the car.
In general, any linear function can be
described in slope-intercept form.
A linear function can be written in the form
y = mx + b, where m is the slope of the line
and b is its y-intercept.
Example 1) The graph of a linear function has slope
3
and y-intercept –4.
5
Write an equation for this function.
3
y= 5 x −4
CHECK YOUR UNDERSTANDING
The graph of a linear function has slope –
7
and y-intercept 2. Write an equation
3
for this function.
7
y= −3 x +2
Example 2) Graph the linear function with
equation: y =
1
x+3
2
CHECK YOUR UNDERSTANDING
Graph the linear function with
3
4
equation: y = – x + 2
Example 3) Write an equation for each of the given linear function below.
m
Example 4) The student council sponsored a dance. A ticket cost $5 and the
cost for the DJ was $300. range
domain
a) Write an equation for the profit, P dollars, on the sale of t tickets.
b) Suppose 123 people bought tickets. What was the profit?
c) Suppose the profit was $350. How many people bought tickets?
d) Could the profit be exactly $146? Justify the answer.
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
the values in the equation form: y = mx + b.
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.