Graphing Linear Equations
m stands for this in y=mx+b
What is Slope?
Type of linear functions which have a slope of zero.
What are Horizontal Lines?
A set or collection of 2 or more equations that you deal with all together at once.
What are Systems of Linear Equations?
In y=mx+b, this is what the b stands for.
What is the y intercept?
What type of slope results in a Line Rising From Left To Right
What is Positive Slope?
This is the symbol in the inequality when you have a dotted line and a solution region below the dotted line.
What is y < mx+b?
This type of line has an undefined slope.
What is a vertical line?
True or False: The solution to a system of inequalities can NEVER be "no solution".
Describe the solution to a system of inequalities.
Graph each individual inequality, and then finding the overlaps of the various solutions.
Given the equation y = -2x + 12 representing the height of a candle burning if it melts 2 inches per hour, what would the starting height be?
12 inches
What is 1.20x + 1.05y = 5.55 ?
Solve: −3y= -6x +15 and y= 2x+8
Is the solution "no solution" or "infinite solutions"?
No solution (parallel lines)
Solve y<2x - 3 and y > -3x + 1
overlap of the two shaded regions
The manager of an electronics store projects that the store should achieve $10,000 in revenue from TVs and DVD players every day in order to remain profitable. Its DVD players sell for $300, and TVs sell for $580. Write an equation statement.
300x + 580y = 10,000
The starting point and slope for the equation
y = -4 .
Start at y = -4, the slope is 0
(so it is a horizontal line)
Solve: 2x + 3y= 35 and x−3y=−5 using substitution.
x=10 y=5
Solve y > 4 and x < -2
Overlap of the shaded regions
Anumeha mows lawns. She charges a service fee and also a constant fee for each hour of work.
F(t) models Anumeha's fee (in dollars) for working t hours.
F(t) =12t + 6. How much does Anumeha charge for each hour of work?
$12 per hour (like the slope of the equation)
Harry deposits money in the bank each month to save for a vacation. He begins with $500 and he deposits $150 to the bank each month. How many months (x) will it take him to have $2000 total (y)?
2000 = 150x + 500
This type of system of equations has infinitely many solutions.
What are the same lines?
Solve x-3y = -13
and 3x+7y = 25.
Hint: Elimination might be easiest!
(-1, 4)