Equations
A student is solving 6x+8=26. They subtract 8 from both sides. What should the next step be?
Divide by 6!
Your final answer is x > -6. Will your number-line graph have an open or closed circle at -6?
Open
A line falls from left to right. Is its slope positive, negative, zero or undefined?
Negative
y=-3/4x+6; Identify m and b
m= -3/4; b=6
True or false: A horizontal line has an undefined slope
False. Zero!
Which x value makes the equation true? 4x-7=13
x=3, x=4, x=5, x=6
x=5
You reach this step: -5x<30. What special rule will take place next?
The inequality will flip when divided by -5.
A line passes through (-4,7) and (5,7). Without using the slope formula, what is the slope?
Zero! The y values stayed the same, which means there are fixed outputs. Fixed outputs mean it is a horizontal line with no slope.
You need to graph y=-2x-5. What do you graph first and where?
-5 on the y-axis
A student solves an inequality and writes x>7. Based on what we have been doing in class, what other TWO things are missing? Show the work!
Number line graph and interval notation!
A student solves:
3(x-4)+5=20
3x-4+5=20
3x+1=20
What did the student do incorrectly?
They distributed incorrectly!
You are given (- infinity, 4]. Write the solution as an inequality and graph.
x is less than or equal to 4; Graph is a closed circle at 4 and shaded left.
A line passes through (3,-5) and (3,8). Is this line horizontal or vertical? What kind of slope does it have?
Vertical with undefined slope!
y=-2x+3; Does the line rise or fall from left to right?
Falls
Without graphing the line, tell me THREE things you know about the graph: y=-3/4x+6
- Slope is -3/4
- y-intercept is 6
- The line is decreasing from left to right
- It has a negative slope
Solve: (2/3)x+5=17
x=18
Solve: 7x-3 <=4x+12
Give your answer as an inequality, graph and interval notation.
x<=5, Graph is a closed circle at 5 and shaded left, (- infinity, 5]
Find the slope of the line passing through (-2,7) and (4,-5)
m=-2
Graph y=-2/3x+4
Begin at (0,4) and slope should go down two, right three
A student is graphing y=-2/3x+4. They say they are going to start at -2 on the y-axis then go up 3 and right 4. Identify TWO errors to their plan!
The y-intercept is 4, so they should start at 4 on the y-axis. The slope is -2/3 not 3/4. So, they should move down 2 and to the right 3.
Two students solve: 4x-7=2x+9. Student A subtracts 2x first and gets x=8. Student B subtracts 4x first and gets x=-8. Who is correct? Explain what went wrong for the other student.
Student A
Ava and Noah solve -4x+3>19. Ava gets x>-4 while Noah gets x<-4. Who is correct and why?
Noah, reversed the inequality!
Two students calculate the slope of the same line. Student A gets -6/3. Student B gets 6/-3. They think they got different answers. Did they? What is the slope of the line, and is it increasing or decreasing?
They are the same! Decreasing!
Graph x=-3
Vertical line through x=-3
Write an equation of ANY LINE that satisfies all three: negative slope, positive y-intercept, not horizontal or vertical.
Many possibilities