Problem 55 - Understanding Elementary Algebra with Geometry

Question

What is the slope of a line that is parallel to the line whose equation is \(y=3 x-8 ?\)

Step-by-Step Solution

Answer

The slope is 3.

Step 1: Identify the Slope of the Given Line

To find the slope of a line parallel to the given line, first identify the slope of the given line. The given line is in the form of the slope-intercept equation, which is written as \(y = mx + b\), where \(m\) represents the slope. In the equation \(y = 3x - 8\), the slope \(m\) is 3.

Step 2: Understand Parallel Lines

Parallel lines have identical slopes. Therefore, if two lines are parallel, their slopes will be exactly the same.

Step 3: Determine the Slope of the Parallel Line

Since we know the lines are parallel and we've identified that the slope of the given line is 3, it follows that the slope of any line parallel to the given line will also be 3.

Key Concepts

slope-intercept form

The slope-intercept form is a way of writing the equation of a line so that you can easily identify the slope and the y-intercept. The formula is written as:

Every time you see an equation like this, ': 'since we know the lines are parallel and we've identified that the slope of the given line is 3, it follows that the slope of any line parallel to the given line will also be 3.