Question

Graph the given equation. $$ 2 x=3 y $$

   Graph the given equation. 
$$
2 x=3 y
$$

Finite Mathematics and Applied Calculus

Finite Mathematics and Applied Calculus

Stefan Waner, Steven… 5th Edition

Chapter 1, Problem 37

Instant Answer

Solved by Expert Gregory Higby

09/23/2021

Step 1

The given equation is $2x = 3y$. Using the symmetric property, we can rewrite this as $3y = 2x$. Show more…

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Graph the given equation. $$ 2 x=3 y $$

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Key Concepts

Graphing Techniques

Graphing a linear equation involves determining at least two points that satisfy the equation and drawing a straight line through them. Common techniques include rearranging the equation into slope-intercept form to identify the slope and y-intercept easily, as well as finding the x-intercept by setting y to zero. These methods provide a systematic approach to visualize the relationship described by the equation on a coordinate plane.

Slope-Intercept Form

The slope-intercept form is a way of writing a linear equation as y = mx + b, where m represents the slope of the line and b represents the y-intercept. This form is particularly useful because it immediately shows the steepness of the line and the point where the line crosses the y-axis, which are both critical for graphing the equation quickly and accurately.

Linear Equation

A linear equation represents a relationship between two variables in which each term is either a constant or the product of a constant and a single variable. Its graph is invariably a straight line, and it is commonly expressed in forms such as the slope-intercept form (y = mx + b) or the standard form (Ax + By = C). This concept is fundamental in algebra as it introduces the idea of a constant rate of change between the variables.

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