In Problems 7-12, use the graph of each linear function to...

In Problems $7-12$, use the graph of each linear function to find the rise, run, and slope. Write the equation of each line in the standard form $A x+B y=C, A \geq 0 .$ (All the horizontal and vertical line segments have integer lengths. )
(GRAPH CANT COPY)

Key Concepts

Standard Form Linear Equation

The standard form of a linear equation is typically written as Ax + By = C, where A, B, and C are integers and A is non-negative. This form is useful for easily determining certain properties of the line, such as intercepts, and for performing algebraic operations, comparisons, and graphing methods that are widely used in algebra.

Graph of a Linear Function

Graphing a linear function involves plotting points that satisfy the linear equation on a coordinate plane and drawing a straight line through these points. It visually represents the relationship between the variables, making the concepts of slope, intercepts, and overall behavior of the function more intuitive and easier to analyze.

Rise and Run

Rise and run are the fundamental components used to calculate the slope of a line, where 'rise' refers to the change in the vertical direction between two points, and 'run' refers to the change in the horizontal direction. Understanding these measurements is essential for interpreting movements along a line and provides a visual understanding of the rate at which a line ascends or descends.

Slope

The slope of a line, often expressed as the ratio of rise over run, quantifies the steepness and direction of a line. A positive slope indicates an upward trend, a negative slope indicates a downward trend, and a zero slope represents a horizontal line. This concept is central in algebra and calculus for analyzing and predicting linear behavior.

Please give Ace some feedback