Linear Equations: Slope and Intercepts

Study Notes

Slope Intercept Key Terms

Y-Intercept: Part of the linear equation represented as y = mx + b, where 'b' signifies the y-value at the point where the line intersects the y-axis.
X-Intercept: Represents points where the graph crosses the x-axis (y = 0). These points occur when the value of y is zero.
Domain: Refers to the set of valid values for the independent variable(s) that result in real outputs (y-values) for a function. Typically includes all x-values that yield real y-values.
Range: Defined as the difference between the maximum and minimum values in a dataset. It can also encompass all output values of a function, representing the span of values a function can produce.
Linear Equation: An algebraic expression where each term consists of a constant or the product of a constant and the first power of a single variable. Linear equations are foundational in mathematics and often appear in various mathematical disciplines.
Non-linear Function: Characterized by equations where the unknowns are part of a polynomial of degree greater than one. Non-linear functions do not produce straight-line graphs.
Linear Function: A specific type of function whose graph is a straight line. Algebraically, it is defined as a polynomial of degree one or a constant horizontal line (y = c).
Constant Rate of Change: Indicates no acceleration; a function exhibiting this trait has a second derivative of zero. Graphically, it appears as a straight line, with a uniform change in y corresponding to changes in x.
Slope: Represents the steepness of a line defined by the rise over run between two points. Various formulas exist to calculate slope, illustrating its significance in determining line steepness in geometry and algebra.

Description

Explore the fundamental concepts of slope and intercepts in linear equations with this flashcard quiz. Understand the definitions of y-intercept and x-intercept, and learn how they are represented in the linear equation y = mx + b.