just the easy stuff
If an inequality has < or >, the line will be...
D-A-S-H-E-D
What is an example of an equation that is a horizontal line?
Y = 5
(3, -3) is located in which quadrant?
IV aka FOUR
Is (-4, 2) a solution to 3/2(x - 4) < -7y
(-4, 2)
3/2((-4) - 4) < -7(2)
-6 - 6 < 14
-12 < 14 TRUE, so (-4, 2) is a solution!
Perpendicular lines slopes are...
the opposite reciprocal
9 > x
Graph it on a number line
1. SWITCH THE SIGN! x < 9
2. Open circle at 9, arrow facing LEFT
When you divide or multiply by a negative number
When the variable is on the right side
What is the x-intercept of this equation:
y = 1/3x + 1
(-3, 0)
Graph and solve
2x - 6 < -1/2(12 - 4x)
2x - 6 < -6 + 2x
-6 < -6 FALSE
NO SOLUTION
Solve. -2/5x + 4 ≥ 2
x ≤ 5
* DOUBLE POINTS *
In the point-slope form of a linear equation, (a, b) represent what?
Be careful with how you word this!
(a, b) represents a point the line will pass through
Is a coordinate on a solid line part of the solution of a systems of inequalities?
YES
(1, -4) (-3, 5)
Using the ordered pairs, what is the slope?
5 - (-4) / -3 - 1
9/-4
Slope = -(9/4)
Graph this on a number line
-4(3x + 1) ≤ 2/3
x ≥ -1/3
Mackenzie is doing some online shopping. Everything is on sale for $14.89. Mackenzie has $50 to spend. The online store charges $6.99 for shipping & handling. Write an inequality to show at MOST how many items Mackenzie could purchase.
Let x = the number of items bought
6.99 + 14.89x ≤ 50
TRUE OR FALSE - Read this carefully
The solution of a systems of inequalities is the shaded area on a graph
FALSE. It is the overlapping shaded area
TRUE OR FALSE
A horizontal line has an undefined slope
false. VERTICAL!
Thomas G and Thomas S are hosting a party. They are buying pizza and ice cream. Pizza costs $12 each and ice cream is $5 each. They can't spend no more than $80.
They know they will be buying at least 6 ice creams. Write an inequality to represent this situation
Let i = ice cream
12p + 5i ≤ 50
y ≥ 5
Henry E needs more cash, he decides to start a babysitting business. He wants to make at least $2,000. He charges $17 per hour.
If he works enough to make $2,000 he will put 40% of it in his savings account.
At minimum, how many hours does he need to work to put $500 in his savings?
Let x = number of hours worked
17x > 2000
x > 118 hours to make $2,000
40% of 2000 is 800. So he actually needs to make MORE than 2,800.
17x > 2800
x > 167 hours
Graph the system and tell me a coordinate that is in the solution area.
-y - 4 > -2x
-8x + 4y ≥ 12
A line has a reciprocal slope of -1/5. What is the slope of a parallel line?
Slope = -5
What is the difference between a solution to a system of equations versus a system of inequalities?
A solution to a system of equations is the coordinate at which the lines intersect. A solution to a system of inequalities, is the overlapping shaded area on a graph.
You and two friends are going apple picking at Carter Mountain. Between the three of you, you can spend a total of $36 and you want to pick at least 5lbs. You all decide to pick Fuji and Granny Smith apples. Fuji apples are $4 per pound and Granny Smith apples are $3 per pound. The three of you also decide to buy a package of apple cider donuts for $6.
Write a system of inequalities and explain a possible solution.
Let x = pounds of Fuji apples
Let y = pounds of Granny smith apples
x + y ≥ 5
4x + 3y + 6 ≤ 36
Simplify the second equation... 4x + 3y ≤ 30