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Chapter 2: Problem 97

Explain how to use the general form of a line's equation to find the line's slope and \(y\) -intercept.

Short Answer

Expert verified
After identifying the values of \(A\), \(B\), and \(C\) in the general equation, calculate the slope using \(-A/B\) and the y-intercept using \(C/B\). Then, express these values in the slope-intercept form of a line equation, \(y = mx + c\).

Step by step solution

01

Identify the terms in the general equation

Given a line's general equation \(Ax + By = C\), identify the values of \(A\), \(B\), and \(C\). These are constant values and may be any real number including zero.
02

Find the Slope

The slope of the line, often denoted as \(m\), is found by the ratio \(-A/B\). Calculate this value for your given line's equation.
03

Find the Y-Intercept

The \(y\)-intercept is the point where the line crosses the y-axis, often denoted as \(c\). This can be found by the ratio \(C/B\). Calculate this value for your given line's equation.
04

Convert to Slope-Intercept Form

With the slope \(m\) and \(y\)-intercept \(c\), you can express the line equation in slope-intercept form, \(y = mx + c\). Write down your line's equation in this form.

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