Equations
Convert to Slope-Intercept Form:
6x + 2y = 20
1. 6x + 2y = 20
2. 2y = -6x + 20
3. y = -3x + 10
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
(In Desmos)
Find A + B
7x^2 + 14x + 21
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
(In Desmos)
Is the following a function? Yes or No and why?
NO because for an x-value or input repeats. For every input or x-value there is not one and only one output. (x = -3 repeats)
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
y = 10x - 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) 17.50 represents the weekly charge for her cell phone plan, 120 represents the total cost of the cell phone plan, and y represents the sign-up fee.
b) 17.50 represents the total cost of her cell-phone plan, 120 represents the sign-up fee for the cell phone plan, and y represents the weekly charge.
c) 17.50 represents the weekly charge for her cell-phone plan, 120 represents the sign-up fee for the cell phone plan, and y represents the total
d) 17.50 represents the sign up fee for her cell phone plan, 120 represents the weekly charge for the cell-phone plan and y represents the weekly charge for her plan.
Annotate
Slope = Rate of Change = 17.50 = weekly charge
Y-Intercept = Start = 120 = sign-up fee
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.
(In Desmos)
Find A - B
3x^2 + 6x + 9
y = 5/9x + 10
Perpendicular Lines = Opposite Reciprocal Slopes
Old Slope = 5/9
New Slope = -9/5
(In Desmos)
Is the following a linear function? Yes or No and why?
YES because there is a constant pattern or rate of addition in the table.
Change in x = +2
Change in y = +6
Slope = 6/2 = 3
(In Desmos)
Solve for x:
Method: Cross-Multiply (Proportional Relationship)
2(15x + 3) = 6(8x - 5)
30x + 6 = 48x - 30
6 = 18x - 30
36 = 18x
x = 2
Domain = All x-values/Inputs
Range = All y-values/Outputs
(In Desmos)
Find C + D
11x^2 + 8x + -20
11x^2 + 8x = 20
(In Desmos)
Annotate the slope and y-intercept of the following graph
Slope = Positive (Uphill Line)
Y-Intercept = Negative (Starts in Middle Below Origin)
(In Desmos)
Which of the following values can be inserted into the blank spot in the table to satisfy the definition of a function? SELECT ALL.
Function: For each input there is one and only one output (x can't repeat)
Answer: A (x = -5) and D (x = 8)
Which of the following equations is perpendicular to
y = 2/3x + 9 and passes through (2, 5)?
a) y = 2/3x + 5
b) y = -2/3x + 8
c) y= -3/2x + 5
d) y = -3/2x + 8
Perpendicular = Opposite Reciprocal Slopes
Old Slope = 2/3
New Slope = -3/2 (eliminate A and B)
Point = (2, 5)
Point-Slope: y - 5 = -3/2(x - 2)
y - 5 = -3/2x - - 3
y - 5 = -3/2x + 3
y = -3/2x + 8
ANSWER: D
Yawo gets a job as NBA player Ben Simmons' new shooting coach. Yawo makes $100 a day and he can work up to 6 days a week. If d represents the number of days Yawo works, and h(d) represents how much money he makes each week, which of the following best represents the domain?
A) [100, 200, 300, 400...]
B) [0, 1, 2, 3, 4, 5, 6]
C) [...-3, -2, -1, 0, 1, 2, 3...]
D) [0, 1, 2, 3, 4, 5, 6, 7, 8...]
Domain = X/Inputs = Days Worked
Negative? NO
Fraction? NO
Zero? YES
Limitation? MAX of 6
ANSWER: B [0, 1, 2, 3, 4, 5, 6]
(In Desmos)
Find C - D
5x^2 + -16x + 60
5x^2 - 16x + 60
Find the x and y intercepts of the following equation...
8x - 2y = 24
X-Intercept:
8x = 24
x = 3
Y-Intercept:
-2y = 24
y = -12
Are the following lines parallel, perpendicular or neither?
y = 2/7x + 8
y = -7/2x - 5
PERPENDICULAR because the slopes are opposite reciprocals