Equations
What is the slope and y-intercept of the equation below?
y = -2x + 9
Slope = -2
Y-intercept = 9 or (0,9)
What is the slope of a line that passes through (3, 10) and (9, 34)?
Answer: 4
Slope = (34 - 10) / (9 - 3) = 24/6 = 4
When we discuss interpreting real-world slope and y-intercept, what annotations should we make for slope and y-intercept?
Slope = Rate of Change
Y-Intercept = Start
Annotate the slope and y-intercept of the graph
(I will draw graph)
Slope = Positive
Y-Intercept = Negative
Solve the equation below for x:
2(x + 6) = 30
Answer: x = 9
1. 2(x + 6) = 30
2. 2x + 12 = 30
3. 2x = 30 - 12
4. 2x = 18
5. x = 9
Convert From Standard Form to Slope-Intercept Form:
40x + 4y = 12
1. 40x + 4y = 12
2. 4y = -40x + 12
3. y = (-40/4)x + 12/4
4. y = -10x + 3
What is the slope of a line that passes through (5, 8) and (1, -4)?
Answer: 3
Slope = (-4 - 8) / (1 - 5) = -12/-4 = 3
Latasha starts a new cell phone plan. The cost of her plan is is represented by by the equation `y=17.50x+120`, where y is the total cost of her cell phone plan for a certain number of weeks, x. In the equation above, which statement correctly represents both the slope and the y-intercept?
a) The slope represents the weekly charge for her cell phone plan and the y-intercept represents the total cost of the cell phone plan.
b) The slope represents the total cost of her cell-phone plan and the y-intercept represents the sign-up fee for the cell phone plan.
c) The slope represents the weekly charge for her cell-phone plan and the y-intercept represents the sign-up fee for the cell phone plan.
d) The slope represents the sign up fee for her cell phone plan and the y-intercept represents the weekly charge for the cell-phone plan.
Annotate
Slope = Rate of Change
Y-Intercept = Start
Answer: C
The slope represents the weekly charge for her cell-phone plan and the y-intercept represents the sign-up fee for the cell phone plan.
Annotate the slope and y-intercept of the graph
(I will draw graph)
Slope = Negative
Y-Intercept = Positive
Are these 2 lines parallel, perpendicular, or neither? Explain your thoughts.
y = 4x - 8
y = 4x + 12
Parallel because they have the same slope and different y-intercepts
Convert From Standard Form to Slope-Intercept Form:
18x - 3y = 6
1. 18x - 3y = 6
2. -3y = -18x + 6
3. y = (-18/-3)x + 6/-3
4. y = 6x + -2
5. y = 6x - 2
Convert from standard form to slope-intercept form:
21x + 3y = 9
1. 21x + 3y = 9
2. 3y = -21x + 9
3. y = (-21/3)x + 9/3
4. y = -7x + 3
Leni is buying cameras to become a YouTube star. He has $300. Cameras cost $30 each. Leni wants to have at least $80 remaining when he finishes. Write an inequality to represent Leni's scenario.
Answer: 300 - 30x >= 80
Start = 300
Change = -30
>= for at least
End = 80
Annotate the slope, y-intercept, and inequality sign of the graph
(I will draw graph)
Slope = Positive
Y-intercept = Positive
< = Less Than = Shaded Below
Are these 2 lines parallel, perpendicular or neither? Show work and explain.
y = -5x + 10
10x + 2y = 16
Parallel because they have same slope and different y-intercept
10x + 2y = 16
2y = -10x + 16
y = -5x + 8
y = -5x + 10
If a = 5, how many solutions does the equation below have?
15x + 12 + 8 = a(3x + 6)
a) One Solution
b) No Solutions
c) Infinite Solutions
b) No Solutions
1. 15x + 12 + 8 = a(3x + 6)
2. 15x + 12 + 8 = 5(3x + 6)
3. 15x + 20 = 15x + 30
Same coefficient, Different constant
What is the slope and y-intercept of the following equation?
24x - 6y = 30
Answer: Slope = 4 and Y-Intercept = -5 or (0,-5)
1. 24x - 6y = 30
2. -6y = -24x + 30
3. y = (-24/-6)x + 30/-6
4. y = 4x + -5
5. y = 4x - 5
300 - 30x >= 80
Can Leni buy 9 cameras? Show your work and explain your answer.
Answer: No
300 - 30x >= 80
x = 9
300 - 30(9) >= 80
300 - 270 >= 80
30 >= 80
FALSE STATEMENT. He will only have $30 left over but needs to have at least $80 left over
Which of the following could be an equation for the inequality? (I will draw)
a) y < -2x - 5
b) y > -2x + 5
c) y > 2x - 5
d) y < 2x + 5
B: y > -2x + 5
(Negative Slope, Positive Y-Intercept, Shaded Above so Greater Than)
Which statement about the function is true? (I will draw graph)
a) f(6) = 8
b) f(-3) = 2
c) f(2) = -8
d) f(-8) = 2
Answer: D
f(-8) = 2
(-8, 2) is a point on the red function
Write the equation of a line that passes through the points (8, -6) and (3, 14)
1. Slope = (14 - -6)/(3 - 8) = 20/-5 = -4
2. Annotate Point-Slope
8 = x = subtraction
-6 = y = addition
3. Write Point-Slope
y + 6 = -4 (x - 8)
4. Solve
y + 6 = -4x + 32
y = -4x + 26
Write the equation of a line that passes through the points (6, 12) and (10, 32)
1. Slope = (32 - 12)/(10 - 6) = 20/4 = 5
2. Annotate Point-Slope
6 = x = subtraction
12 = y = subtraction
3. Write Point-Slope
y - 12 = 5(x - 6)
4. Solve
y - 12 = 5x - 30
y = 5x - 30 + 12
y = 5x - 18
300 - 30x >= 80
What is the maximum number of cameras Leni can buy? Show your work and explain your answer.
Answer: 7 cameras
1. 300 - 30x >= 80
2. -30x >= 80 - 300
3. -30x >= -220
4. DIVIDE BY -30 and FLIP SIGN
5. x <= 7.33
If Leni buys more than 7 cameras, he won't have at least $80 left over.
Which of the following could be an equation for the scatterplot? (I will draw)
a) y = -3x - 6
b) y = -3x + 6
c) y = 3x - 6
d) y = 3x + 6
Answer: C
y = 3x - 6
Positive Slope, Negative Y-Intercept
Which of the following is parallel to y = 3x + 6. Show your work.
a) 6x + 2y = 20
b) 15x - 5y = 10
c) 2x + 6y = 20
d) 15x - 5y = 20
Answer: B
15x - 5y = 20
1. -5y = -15x + 20
2. y = -15/-5x + 20/-5
3. y = 3x + -4
Same slope (3), Different y-intercept