Question

Linear Equations, Graphs, and Functions $4 x-y=0$

   Linear Equations, Graphs, and Functions
$4 x-y=0$

Intermediate Algebra

Intermediate Algebra

John Hornsby; Terry… 13th Edition

Chapter 2, Problem 46

Instant Answer

Solved by Expert Khalida Dawar

03/18/2022

Step 1

The equation becomes: \[4x - 0 = 0\] Solving for x, we get: \[x = 0\] Show more…

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Linear Equations, Graphs, and Functions $4 x-y=0$

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Key Concepts

Linear Equations

A linear equation represents a straight line in the coordinate plane and is typically expressed in forms such as Ax + By + C = 0 or y = mx + b. It shows a constant rate of change between the variables and is foundational in algebra for understanding relationships between variables.

Graphing Linear Equations

Graphing a linear equation involves plotting all the points that satisfy the equation, resulting in a straight line. The line's direction and position are determined by its slope and intercepts, providing a visual representation of the equation.

Slope

The slope of a line is a measure of its steepness and direction, defined as the ratio of the change in the y-coordinate to the change in the x-coordinate between any two points on the line. It indicates how much y changes for a unit change in x.

Y-intercept

The y-intercept is the point at which a line crosses the y-axis. In the slope-intercept form of a linear equation (y = mx + b), the constant b represents the y-intercept, highlighting the starting value of the function when x is zero.

Function

A function is a special type of relation where each input from the domain corresponds to exactly one output in the range. In the context of linear equations, when the equation is written in the form y = mx + b, it defines a linear function that assigns a unique y-value to each x-value.

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