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Chapter 0: Problem 32

Find an equation of the line: with slope \(-5,\) containing \((5,0).\)

Short Answer

Expert verified
The equation of the line is \( y = -5x + 25 \).

Step by step solution

01

Understand the slope-intercept form

The slope-intercept form of a line is given by the equation: \( y = mx + b \) where \(m\) is the slope and \(b\) is the y-intercept.
02

Identify the given information

From the problem, the slope \(m\) is given as \(-5\) and the point \((5, 0)\) lies on the line.
03

Substitute the slope into the slope-intercept formula

Plug the slope value into the slope-intercept formula: \( y = -5x + b \).
04

Use the given point to find the y-intercept

Substitute the point \((5, 0)\) into the equation \( y = -5x + b \) to find \( b \). This gives: \( 0 = -5(5) + b \). Solve for \(b\): \( 0 = -25 + b \) \( b = 25 \)
05

Write the final equation

Substitute \( b = 25 \) into the slope-intercept formula: \( y = -5x + 25 \).

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

slope-intercept form
The slope-intercept form is one of the most popular ways to write the equation of a line. It is expressed as:
\( y = mx + b \)
In this equation:
  • \

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