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Chapter 1: Problem 18

Find an equation of the given line. Slope is \(2 ; x\) -intercept is \(-3\).

Short Answer

Expert verified
The equation of the line is \( y = 2x + 6 \).

Step by step solution

01

Understand the information given

The slope of the line is given as 2. The x-intercept of the line is given as -3.
02

Use 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.
03

Find the y-intercept

Since the x-intercept is -3, the line passes through the point \( (-3, 0) \). Substitute the slope (2) and the point \( (-3, 0) \) into the point-slope formula to find the y-intercept \( b \). \[ y = mx + b \] \[ 0 = 2(-3) + b \] \[ 0 = -6 + b \] Solving for \( b \), we get \[ b = 6 \]
04

Write the final equation

Substitute the slope (2) and the y-intercept (6) back into the slope-intercept form equation: \[ y = 2x + 6 \]

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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 of a line is a simple and powerful equation to describe a straight line. It is written as:
\[ y = mx + b \]
In this formula,
  • \

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