Vocabulary and Definitions
What is a variable?
a symbol for a number we don't know yet
How do you write in slope-intercept form?
y=mx+b
What is the y-intercept of the following line?
y<3/4x - 1
-1
18 + 7n +3 +6n ≤ 86
n ≤ 5
What are the first things you should do when reading a word problem?
Read all of it,
highlight or circle key words
Identify your variables
What is slope?
Rise over run, the change in y over the change in x
When do I shade above the line?
When y is greater than
What is the slope of the following line?
y> -1/2x + 4
-1/2x
3(x-2) > 21
x > 9
2
What is the y-intercept?
The constant in y=mx+b form.
It is where you plot your point on the y-axis.
When do I shade below the line?
When y is less than
Go down two, to the right three
-2(y+3)≤12
y≥9
When can you use a system of inequalities in real life?
Inequalities are used for comparison. “He is taller than me.” or “The iPhone with larger memory capacity is more expensive.”. A more complicated example is also with calculating your driving speed.
What is the solution region?
The solution of a linear inequality is the ordered pair that is a solution to all inequalities in the system
When is my line dashed?
When inequality is just "less than" or "greater than"
What do we call it when we multiply within the parentheses?
DISTRIBUTION
-5x+4(x-2)<0
x>-8
Write the two inequalities for the following word problem:
Michelle works at two jobs. She makes $4 an hour babysitting, and $6 an hour working at the grocery store. She wants to make more than $48 a week, but she has to work less than 11 hours a week.
x= hours babysitting
y= grocery store
4x+6y>48
x+y<11
What are systems of equations?
A system of equations is a collection of two or more equations with a same set of unknowns
When is my line solid?
When my inequality is "less than or equal to" or "greater than or equal to"
What happens when I divide or multiply by a negative number?
The inequality sign flips.
6-4(6n+7)≥122
n≤-6
Graph
y<-1/2x+5
y≥-x+4
Look at algebra 7.6, very last page of practice packet