Problem 76 - Intermediate Algebra

Question

Find the slope of each line. The line with equation \(y=-3 x+4\)

Step-by-Step Solution

Answer

The slope of the line is -3.

Step 1: Identify the Slope-Intercept Form

Recognize that the given equation \(y = -3x + 4\) is in the slope-intercept form \(y = mx + b\), where \(m\) represents the slope and \(b\) represents the y-intercept.

Step 2: Extract the Slope

In the equation \(y = -3x + 4\), compare it to the general form \(y = mx + b\). Here, \(m = -3\), indicating the slope of the line.

Key Concepts

Understanding Linear Equations

Linear equations are fundamental in algebra. They describe a straight line on a graph. Such equations measure relationships between two variables, typically expressed in the form of \(y = mx + b\).
Here, \(m\) is the slope and \(b\) is the y-intercept.

• The slope \(m\) signifies the tilt or steepness of the line.
• The y-intercept \(b\) is where the line crosses the y-axis.

Linear equations are easy to work with since they create a predictable and uniform graph. Understanding them is essential, as they are the foundation of many mathematical concepts beyond basic algebra.

Exploring the Slope-Intercept Form

The slope-intercept form of a linear equation is one of the most practical and commonly used formats in algebra. It looks like \(y = mx + b\).
In this format, the slope \(m\) tells you how quickly the line rises or falls as you move along it, while the y-intercept \(b\) tells you the exact point where the line crosses the y-axis.

• When \(m > 0\), the line ascends as it moves from left to right.
• When \(m < 0\), the line descends.
• If \(m = 0\), you have a horizontal line.

The slope-intercept form allows for quick identification and graphing of a line, making it a key tool in both simple and complex algebraic problems.

Your Guide to Algebra Tutorials

Algebra tutorials often start with linear equations and the slope-intercept form because they are straightforward and efficient.
These tutorials break down algebra into bite-sized lessons to ease learning.
To effectively understand and use algebra tutorials involving linear equations:

• Follow each step and note how the equation is transformed.
• Make sure to practice by solving similar problems.
• Fully grasp terms like slope and y-intercept for greater success.

These guides simplify algebraic concepts and help strengthen your foundational understanding, preparing you for more advanced topics in mathematics.