Transcript Day Problems • Graph each function by translating y = | x |. 1.

Day Problems
• Graph each function by translating y = | x |.
1. y = | x | + 3
2. y = | x | - 4
•
Write an equation for the translation of
y = | x |.
3. 9 units up
• Graph each function by translating y = | x |.
4. y = | x – 2 |
5. y = | x + 5 |
• Write an equation for each translation of y = | x |.
6. left 4 units
7.1 Solving Systems by Graphing
• System of linear equations - two or more
linear equations together.
– One way to solve a system of linear equations is by
graphing each equation.
• Look for any point common to all the lines.
• Solution of the system of linear equations –
any ordered pair in a system that makes all
equations true.
Solving a System of Equations
• Solve by graphing.
y = 2x – 3
y=x–1
• Step 1 – Graph both equations on the same
coordinate plane.
2x – 3
x–1
(2 , 1)
Solving a System of Equations
• Find the point of intersection.
• The lines intersect at (2 , 1), so (2 , 1) is the
solution of the system.
• CHECK!!! See if (2 , 1) makes both equations
true.
• y = 2x – 3
1 = 2(2) – 3
1=4–3
1=1
• y=x–1
1=2–1
1=1
Analyzing Special Types of Systems
• When two lines are parallel, there are no points
of intersection.
• So, a system of linear equations has no
solution when the graphs of the equations are
parallel.
Systems with No Solutions
• Solve by graphing.
y = -2x + 1
y = -2x – 1
y = -2x - 1
y = -2x + 1
The lines are parallel, so there is no solution.
Systems with Infinitely Many Solutions
• Solve by graphing.
2x + 4y = 8
y  
1
x 2
2
The graphs are the same line. There are infinitely many
solutions.
Numbers of Solutions of Systems
of Linear Equations
• Different slopes – the lines intersect, so there is
one solution.
• Same slope, different y-intercepts – the lines are
parallel, so there are no solutions.
• Same slope, same y-intercept – the lines are the
same so there are infinitely many solutions.
More Practice!!!
• Textbook – p. 343 #2 – 22 even – finish for
homework.