Linear Legends
What is the formula used to find the slope (m) between two points (x₁, y₁) and (x₂, y₂)?
m = (y₂ - y₁)/(x₂ - x₁)
What is the relationship between the slopes of two parallel lines?
They have the same slope.
When graphing the inequality y ≤ 2x + 1, should the boundary line be solid or dashed?
Solid
What is the standard form of a quadratic function?
ax² + bx + c
In the exponential function y = a(b)ˣ, which variable represents the "starting value" or "initial amount"?
a
In the slope-intercept form equation y = 4x - 7, what is the slope and what is the y-intercept?
Slope = 4; Y-intercept = -7
If a line has a slope of 3, what is the slope of a line perpendicular to it?
-1/3
In a system of linear inequalities, what do we call the overlapping shaded region where all possible solutions exist?
The feasible region.
In a quadratic graph (parabola), if the leading coefficient a is negative (a < 0), does the parabola open up or down?
It opens down.
Does the function y = 500(0.8)ˣ represent exponential growth or exponential decay?
Decay (because b is between 0 and 1).
A gym charges 20 to join and 15 per month. Write a linear equation in y = mx + b form to represent the total cost (y) for x months.
y = 15x + 20
Line 1 has the equation y = 2x + 1. Line 2 has the equation 2y = 4x - 6. Are these lines parallel, perpendicular, or neither?
Parallel (after rewriting Line 2 as y = 2x - 3, both have a slope of 2).
If you graph two inequalities and their shaded regions do not overlap at all, how many solutions does the system have?
No solution.
Use the vertex formula x = -b / 2a to find the x-coordinate of the vertex for y = x² - 4x + 1.
x = 2
Which type of rigid transformation "flips" a figure across a line (like the x-axis or y-axis)?
Reflection
How can you tell if a relationship is not linear from its equation? (Give at least two signs).
If it has x², x³, √x, or variables in the denominator.
Write the equation of a line parallel to y = 4x - 1 that passes through the point (2, 3).
y = 4x - 5
Translate this word problem into an inequality: "A student must study at least 5 hours but no more than 12 hours."
5 ≤ x ≤ 12
Factor the quadratic expression x² + 5x + 6.
(x + 2)(x + 3)
What are the four main triangle congruence theorems listed in the study guide?
SSS, SAS, ASA, and AAS, with HL used for right triangles.
What are the two main requirements for a relation to be considered a function?
Every x-value has only one y-value, and it must pass the "vertical line test"
A road has a slope of 2. If a second road is built perpendicular to it, what is the slope of the second road?
-1/2
Solve this system of equations using substitution or elimination: y = 2x + 1 and y = x + 4.
(3, 7)
What part of the quadratic formula (b² - 4ac) tells you if there are two real solutions, one real solution, or no real solutions?
The discriminant.
A population starts at 200 and increases by 10% each year. Write the exponential equation for this situation.
y = 200(1.10)ˣ