Linear Functions
Solving Equations
Inequalities
Systems of Equations
RANDOM!
100
What are the equations for the following linear forms: Slope-Intercept Form Point Slope Form
Slope-Intercept: y = mx + b Point-Slope: y - y1 = m(x - x1)
100
Solve the following equation for x: 2x + 5 = -4x + x - 5
x = -2
100
What are the two differences between the line y = x and the inequality y < x ?
1. The line is dotted (points on the line are not solutions) 2. The graph is shaded below the line (points below the line satisfy the inequality)
100
Solve the following system of equations by graphing: y = 2x + 5 y = (-5/2)x + 14
(2, 9)
100
What is the vertical line test? What is it used for?
The vertical line test is used to test whether a graph is a function or not. If a graph passes the vertical line test, this means a vertical line could be placed through the graph at any point and this line would only touch ONE point on the graph, and is thus a function.
200
Using finite differences, find the function in slope intercept form x - 2, 3, 4, 5, 6 y - 5, 7, 9, 11, 13
y = 2x + 1
200
Solve the following equation for x: 2(x - 3) = 4x / (1 - (-2))
x = 9
200
Graph the following inequality: y ≥ x - 4
y-intercept: (0, -4) slope: 1 solid line, shaded above
200
Solve the following system of equations by substitution: -5x + y = -2 -3x + 6y = -12
(0, -2)
200
Define domain. Define range. You MUST use the words input and output.
Domain - All possible x-values. All values that can be input into a function. Range - All possible y-value. All values that the function can output.
300
What is the function, in slope-intercept form, of the line that passes through the following points: (4,6) and (-4,0)
y = (3/4)x + 3
300
Solve the following equation for A: ABC = DEF - GH
A = (DEF - GH) / BC
300
Graph the following inequality: 2y > x - 6
y-intercept: (0, -3) slope: 1/2 dotted line, shaded above
300
Solve the following system of equations by elimination: -5x - 8y = 17 2x - 7y = -17
(-5, 1)
300
Are these two formulas the same? Prove using Algebra! 1.) A = BC + F 2.) F = A / BC
Not the same! 1.) F = A - BC 2.) A = BCF
400
Find the x-intercept and y-intercept of the following function: y - 4 = (1/2)(4x + 2)
y-intercept: (0, 5) x-intercept: (-5/2, 0) or (-2.5, 0)
400
Solve the following equation for A: A^2 - BC = (DEF) / (GH)
A = √(DEF/GH)+BC
400
Which quadrant is completely shaded on the graph of the following inequality: (Show the graph!) 2x + y ≤ 3(x + 1)
Quadrant 4
400
The senior classes at high school A and high school B planned separate trips to New York City. The senior class at high school A rented and filled 8 vans and 8 buses with 240 students. High school B rented and filled 4 vans and 1 bus with 54 students. How many students does 1 van carry? How many students does 1 bus carry?
Van - 8 Students Bus - 22 Students
400
Are these two formulas the same? 1.) 2ABC / DE = F + G 2.) E = 2ABC / (D(F+G))
YES!
500
Which of the following are NOT functions? Why? 1.) x - 1, 1, 2, 4 3.) 2x +1 = 5 y - 1, 2, 4, 5 2.) x + y = 5 4.) y = 1/2
1 - Two outputs for the input of 1 3 - x=2 is a vertical line, does not pass vertical line test
500
Solve the following equation for x: ABx - DFx = 5
x = 5 / (AB - DF)
500
Graph the following inequality: 2x - 4y > -5(x + 4)
y-intercept: (0, 5) slope: 7/4 dotted line, shaded below
500
Johnny is in a race against his friend Jack. Johnny has traveled 20 miles and is currently traveling 60 mph. Jack has traveled 5 miles and is currently traveling 65 mph. How many hours will it take for Jack to catch up to Johnny? How far will they have traveled?
3 hours 200 miles
500
Solve the following for x by factoring: y = x^2 - 6x + 9
y = (x-3)^2 x=3
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