Algebra 1 Slopes Flashcards

Study Notes

Slope Concepts in Algebra 1

Slope Formula: Represents the rate of change; calculated using Y2-Y1/X2-X1.
Slope-Intercept Formula: Used for linear equations; formatted as y=mx+b, where m is the slope and b is the y-intercept.
Standard Form of Linear Equations: A common way to express linear equations, given as Ax + By = C, where A, B, and C are constants.

Graphing Linear Equations

To graph linear equations, first convert to slope-intercept form.
Start by plotting the y-intercept at the point (0,b).
Use the slope to determine additional points, employing the rise/run method.
Draw a line through the points using a ruler, adding arrows at both ends to indicate continuation.

Types of Slopes

Positive Slope: Indicates that as x increases, y also increases.
Negative Slope: Indicates that as x increases, y decreases.
Zero Slope: Represented by a horizontal line, indicating no change in y as x varies.
Undefined Slope: Associated with vertical lines, where x remains constant regardless of y.

Key Definitions

Rise: Refers to the vertical change between two points on a graph.
Run: Stands for the horizontal change between two points on a graph.
Y-intercept for the equation "3x - 2y = -14" is found at (0, 7) after rearranging into slope-intercept form.

Slope-Intercept Form Example

Given a slope of 2 and a y-intercept of (0, -1), the equation translates to y = 2x - 1.

Point Placement When Graphing

When graphing a point, begin by placing it at the y-intercept.

Slope Calculation Example

For the equation "3x - 2y = -14", the slope, after manipulation, is calculated as 3/2.

Description

Enhance your understanding of slopes with these flashcards. Each card defines key concepts like the slope formula, slope-intercept formula, and techniques for graphing linear equations. Perfect for Algebra 1 students looking to master slope-related topics.