Problem 86 - College Algebra

Question

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

Step-by-Step Solution

Answer

The slope \(m\) and the \(y\)-intercept \(c\) can be identified directly from the general form of a line's equation \(y = mx + c\). \(m\) is the coefficient of \(x\) and represents the slope, while \(c\) is the constant term and represents the \(y\)-intercept.

Step 1: Identify The General Form

The general form of a line's equation is given as \(y = mx + c\). It's crucial to be able to identify this form in any equation given.

Step 2: Identify The Slope

The coefficient of \(x\) in our equation, \(m\), represents the slope of the line. The slope tells us the steepness of the line, including if the line is ascending (positive slope) or descending (negative slope).

Step 3: Identify The y-intercept

The constant term in our equation \(c\) is the \(y\)-intercept. It represents the point where the line crosses the \(y\)-axis. The \(y\)-intercept indicates the value of \(y\) when \(x = 0\).