Graphing
What do you graph to solve a system?
Two Lines in y=mx+b form
What is a solution?
A point that satisfies both equations
Is (2, 3) a solution to y= x + 1?
Yes.
3 = 2 + 1
3 = 3
The solution is where the lines meet
True
What happens if two lines are exactly the same?
Infinitely many solutions
What do you call the point where two lines cross?
The Intersection (AKA the solution)
What form do the two numbers in an ordered pair take?
(x, y)
(horizontal, vertical)
Solve by graphing:
y = x + 2
y = x + 5
No Solution
(Parallel Lines)
A solution is written as an ordered pair
True
What do you do after graphing both lines?
Find their intersection point (IF one exists).
If two lines cross, how many solutions are there?
One Solution
What does a "system" mean in math?
A group of equations
Solve by graphing:
y = x + 4
y = -x + 2
Solution (-1,3)
All systems have one solution
False
What does the solution tell you?
Where both equations are true
How many different solution types are there?
1) One solution
2) No solution
3) Infinitely many solutions
What form is this equation in: y= 2x + 3?
Slope-intercept form
Solve by graphing:
y = -x + 2
-4y = 4x - 8
(Same line)
The solution must make both equations true
True
Explain why parallel lines have no solution
They never intersect, so there is no point that satisfies both equations
If two lines lie on top of each other, what does the graph show?
Infinitely many solutions
What does the slope tell you about a line?
How steep it is, how much it rises or falls
Solve by graphing:
y = (1/3)x - 4
y = (-7/3) x + 4
(3, -3)
Lines with the same slope will always interesect
False
Create a system of equations that has one solution. Graph and explain
Given this equation
y = -x + 5
Show me your graphs and your equations