12/7 and 12/8: 3.10 Getting Started with Equations and Their Graphs
Launch: How many solutions do each of the following equations
a.) 3x +2 = 5x + 3
b.) 3x + 3 = 3x + 3
c.) 3x + 3 = 3x ‐ 3
d.) | x | = 15
Determining the How many solutions does the following equation
Solution for 2 have?
Variable Equations: 2x + 3y = 12
Find four points that satisfy the equation above.
What is the easiest way to view ALL of the solutions?
Introduction to Graph the following equation on your TI‐Nspire:
Graphing equations: y = x2 ‐ 3x + 2
1.) Press HOME and then 6: NEW DOCUMENTS
(Do NOT Save)
2.) Add 2: GRAPHS & GEOMETRY
3.) Enter in the equation after "f1(x) =" and then press
What shape is the graph?
What values of x make y =0 in this equation? Explain.
( Press MENU then WINDOW. Choose 3: Zoom‐In. Move
your cursor to the middle of the U and press enter. Then
Apply the transformation (x,y) → (x +5, y) to each point on
the graph of y = x2 ‐3x + 2. Sketch the resulting graph on
your graph paper. What is the equation of the new graph?
3.11 Equations as Point Testers
Using Equations as What are two points that do not satisfy the following
Point Testers equation? 2x + 3y = 12
Points that pass the test...
Points that fail the test...
Graph of An The collection of all points with coordinates that make
Equation: the equation true.
Graphing Vertical Draw the graph of the equation y = ‐1.
and Horizontal Lines:
Draw the graph of a horizontal line that passes through
point (3, 7). Also, write an equation for the line.