Direct variation is a relationship where y = kx for some number k that is not 0. The number k is the constant of variation. When x doubles, y doubles too. The graph is a straight line through the origin. For example, in y = 3x, the constant is 3.
Parallel and perpendicular lines can be spotted by their slopes. Parallel lines have the same slope, so they never meet. Perpendicular lines cross at a right angle, and their slopes are opposite reciprocals. For example, a line with slope 2/3 is perpendicular to a line with slope −3/2.
The standard form of a linear equation is Ax + By = C, where A, B and C are integers and A is not negative. An example is 2x + 3y = 12. The x- and y-terms are on the left, and the number is on the right. This form makes intercepts easy to find.
Point-slope form is a way to write the equation of a line when you know its slope and one point on it. The form is y − y1 = m(x − x1), where m is the slope and (x1, y1) is the point. For slope 3 through (2, 5), the equation is y − 5 = 3(x − 2).
The key features of a function are facts you can read from its graph. They include where it crosses the axes (the intercepts), its highest or lowest point (maximum or minimum), where it goes up or down (increasing or decreasing), and where it is above or below the x-axis (positive or negative).
The domain of a function is the set of all its inputs, the x-values. The range is the set of all its outputs, the y-values. To find them, list the x- and y-values in a set of points or a table. On a graph, see how far it reaches left to right (domain) and bottom to top (range).
Function notation is a way to name a function and show its input. In f(x) = 2x + 3, f is the name of the function, x is the input, and f(x) is the output. To evaluate f(4), replace x with 4: f(4) = 2(4) + 3 = 11.
A relation is any set of ordered pairs that links inputs to outputs. A function is a relation where each input has exactly one output. To tell if a relation is a function, check that no input repeats with a different output. On a graph, use the vertical line test.
To solve an absolute value inequality, get the absolute value alone, then rewrite it. |x| < 3 means −3 < x < 3 (an “and” inequality). |x| > 3 means x < −3 or x > 3 (an “or” inequality).
To solve an absolute value equation, get the absolute value alone, then split it into two equations. For example, |x − 2| = 5 means x − 2 = 5 or x − 2 = −5, so x = 7 or x = −3.