Problem 39 - Understanding Elementary Algebra with Geometry

Question

Determine the slope of the line from its equation. $$y=-3 x-1$$

Step-by-Step Solution

Answer

The slope is \( -3 \).

Step 1: Understand the Equation Form

Identify that the given equation is in the slope-intercept form, which is represented as \[ y = mx + b \]. In this form, \( m \) is the slope and \( b \) is the y-intercept.

Step 2: Identify the Slope

Compare the given equation \( y = -3x - 1 \) to the slope-intercept form \( y = mx + b \). Here, the coefficient of \( x \) is \( -3 \), which represents the slope \( m \).

Step 3: Conclusion

From the comparison, it is clear that the slope \( m \) of the line is \( -3 \).

Key Concepts

Understanding the Slope-Intercept Form

The slope-intercept form of a linear equation is a crucial concept in algebra. It is represented as \( y = mx + b \). This form clearly indicates the slope and the y-intercept of the line.

• Slope (\