Question

Given the equation $2 x+3 y=4$, answer the following questions. a. Is the slope of the line described by this equation positive or negative? b. As $x$ increases in value, does $y$ increase or decrease? c. If $x$ decreases by 2 units, what is the corresponding change in $y$ ?

Name: Problem 32, Chapter 2: Applied Mathematics: For the Managerial, Life, and Social Sciences
Uploaded: 2021-05-11T06:15:31-08:00
Duration: 5 min
Channel: Naresh Bagrecha
Description: Given the equation 2 x+3 y=4, answer the following questions. a. Is the slope of the line described by this equation positive or negative? b. As x increases in value, does y increase or decrease? c. If x decreases by 2 units, what is the corresponding change in y ?

   Given the equation $2 x+3 y=4$, answer the following questions.
a. Is the slope of the line described by this equation positive or negative?
b. As $x$ increases in value, does $y$ increase or decrease?
c. If $x$ decreases by 2 units, what is the corresponding change in $y$ ?

Applied Mathematics: For the Managerial, Life, and Social Sciences

Soo T. Tan 5th Edition

Chapter 2, Problem 32

Instant Answer

Solved by Expert Naresh Bagrecha

05/11/2021

Step 1

To find the slope of the line, we can rewrite the equation in the slope-intercept form, which is $y = mx + b$, where $m$ is the slope and $b$ is the y-intercept. Show more…

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Given the equation $2 x+3 y=4$, answer the following questions. a. Is the slope of the line described by this equation positive or negative? b. As $x$ increases in value, does $y$ increase or decrease? c. If $x$ decreases by 2 units, what is the corresponding change in $y$ ?

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Key Concepts

Linear Equation

A linear equation represents a relationship between two variables where the graph produced is a straight line. It typically takes forms such as the slope-intercept form (y = mx + b) or the standard form (Ax + By = C), and it illustrates a constant rate of change between the variables.

Slope

The slope is a measure of the steepness and direction of a line, calculated as the ratio of the vertical change (rise) to the horizontal change (run). In a linear equation brought to the form y = mx + b, the slope is represented by m. A negative slope means that as x increases, y decreases.

Rate of Change

The rate of change in the context of a linear equation refers to how much the dependent variable (y) changes for a change in the independent variable (x). Because the relationship is linear, this rate (the slope) is constant, allowing predictions of how any specific change in x will affect y.

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