Math 098
Section 8.1 – Graphing and Writing Linear Functions
Objectives:
1. Graph linear functions
2. Write equations of linear functions
3. Write equations of parallel and perpendicular lines
4. Use linear graphs and equations as models in applications
Graphing Linear Functions
Ex/. The function 𝑓(𝑥) = 5𝑥 + 3 is a model for Lisa’s distance (in feet) from her home as she runs for 𝑥
seconds. Make a table of inputs and outputs.
𝑥
𝑦
(number of seconds)
(total feet from home)
Graph the linear function and consider the domain of the function.
In your function’s equation 𝑓(𝑥) = 5𝑥 + 3, what does the 5 mean for Lisa’s situation? What does the 3 mean
for her situation???
Math 098
Section 8.1 – Graphing and Writing Linear Functions
Definition: The slope of a linear function is a _____________ of change of y-units per x-units.
Graphically, it is _____________ over ____________.
Given two points ______________ and ______________, the slope is 𝑚 =
Definition: A linear function is a function of the form:
(also called the slope-intercept form of the equation of a line)
Ex/. Graph the linear function 2𝑥 + 𝑦 = −6
By using at least two ordered pairs…
By using intercepts…
By using the slope and y-intercept…
Math 098
Section 8.1 – Graphing and Writing Linear Functions
Definition: The point-slope form for the equation of a line is:
Ex/. Write the equation of the line through the points (2, 5) and (−1, −1). Write your equation in function
notation.
Ex/. Write the equation of the line through the points (1, 3) and (6, 3). Write your equation in function
notation.
If the above ordered pairs represented Lisa’s seconds (x-values) and feet from her home (y-values), what would
this equation and graph indicate about Lisa’s situation???
Ex/. On the axes below, graph the line given by 𝑔(𝑥) = 5𝑥 + 1, along with Lisa’s original graph from page
one of these notes.
Compare these two situations. What would these
mean for two different people running from home?
Compare their slopes. What kind of lines are these?
Math 098
Section 8.1 – Graphing and Writing Linear Functions
Property:
Parallel lines have the ___________________________.
Perpendicular lines have ____________________________________.
Ex/. Write the equation of the line passing through (−2, 5) and perpendicular to the line 2𝑥 + 𝑦 = 6. Then
write your equation in standard form: 𝐴𝑥 + 𝐵𝑦 = 𝐶.
Ex/. Write the equation of the line passing through (3, −1) and (3, 8). What do you notice? What is the
slope of this line?
Write the equations of the lines given below. What are their slopes? Are they functions? Explain.