Graphing Inequalities
Verbal Statements
Solution Check
Linear or Nonlinear
Coordinate Plane
100
Less than (or equal to) goes to the _____
Greater than (or equal to) goes to the _______
Left
Right
100
What do each of these phrases have in common regarding translating verbal statements: The sum of, The Difference of, The Product of, The Quotient of.
Each of these phrases mean that we have parentheses (...)
100
The 2 things we need to do when we check if a value or a set of values is a solution set...?
____________ and ________
Substitution and evaluate
100
What in this image tells us it is linear? DOUBLE POINTS IF YOU CAME NAME 2 THINGS!
1. A straight continuous line
2. The equation has 2 variables to an exponent of 1
100
What are the names of:
1) A point that lies on the x-axis
2) A point that lies on the y-axis
1)x-intercept
2)y-intercept
200
Explain the difference of when you use an open circle or a closed circle on a number line for graphing an inequality.
When it is less/greater than, you use an open circle because that value is not a part of the solution set. The closed circle is used for less/greater than OR EQUAL TO. This means that the value in the inequality IS a part of the solution set.
200
Translate to an equation:
Double a number plus 3 is 15
2n + 3 = 15
200
Check if x = -3 is a solution to -2x + 6 = 12 (must show all work for full credit)
Yes
200
Is the equation y=1/x a linear equation? Explain your answer
No, the variable x in the denominator means that the variable is raised to an exponent of -1
200
Name the quadrant: Start at (-2, -3)... go up 4, to the right 12, down 8, reflect across the x-axis, reflect across the y-axis. Where are you?
Quadrant II
300
Make a graph of the inequality.... x < 7
Look to whiteboard, I will draw.
300
Translate to an inequality:
A number decreased by 7 is less than 12
x-7<12
300
Solve and check if the provided solution set is true for the inequality problem below...
-2(3x+4)+5>7-x where x < -2 is the solution set
Yes, because any value LESS THAN -2 makes the inequality true.
300
2x+3y-2(x+3)=-8y+2(-y-3.5) +3 is it linear?
Yes!
300
Plot the points: (4, 1), (-8, 3), (0, -2), (3.5, -.5), and (6, 7) :)
I will come around and look at all board. 60 points/correct ordered pair graphed correctly
400
Solve and graph the solution to: MUST DO BOTH CORRECT FOR FULL CREDIT (can get partial)
-2x+9le27
Solution: x ge -9
I will graph on number line
400
Translate to an inequality:
4 more than 3 times a number is no more than twice the same number minus 11.
3x+4le2x-11
400
Is x = 8 a solution to the given equation?
4(2x-3)+5=3(x+6)
No, x = 5
400
Is this linear? Explain why or why not for full points
No. The graph is a straight continuous line, but the line that has been graphed is x = -3 which only has one variable meaning it cannot be linear.
400
Graph the linear equation: y=2x-7
Will show on board
500
DOUBLE POINTS: Solve and graph on a number line
3(x-4)+18>0
x > -2
500
Translate: Four time the difference of a number and 3 is increased by twice the number plus 5. The result is the same as the a number decreased by one third of the sum of a number and 18
4(x-3)+(2x+5)=x-1/3(x+18)
500
Determine whether the ordered pair (3/2, -4) is a solution to the linear equation 8x + 6y = -12
Yes
500
Which representation is linear: y=3/x-2 ; a curve that increases at a constant rate and goes through (0,1), (2, 4), and (3, 9); 4x-7y=21 ; or
4x-7y=21 because it is an equation w/ 2 variables to an exponent of 1 & the others do not align with rules for being a linear equation
500
TRIPLE POINTS: Graph the 2 given linear equations, AND define their point of intersection
Will display graph on board; intersection as well