Problem 67 - Introductory Algebra for College Students

Question

Describe how to find the slope and the \(y\) -intercept of a line whose equation is given.

Step-by-Step Solution

Answer

To find the slope and the y-intercept of a line given its equation, identify the coefficient of \( x \) as the slope and the standalone number as the y-intercept.

Step 1: Identify the slope

The slope of the line is represented by \( m \) in the equation \( y = mx + b \). This is the coefficient of \( x \). To find it, simply identify the number multiplied by \( x \) in the equation.

Step 2: Identify the y-intercept

The y-intercept of the line is represented by \( b \) in the equation \( y = mx + b \). This is usually a standalone number or constant in the equation without an \( x \) attached to it. To find it, identify this term in the given equation.

Step 3: Interpret the information

Once you have the values of \( m \) and \( b \), you now have the slope and the y-intercept of the line, respectively. The slope tells you the direction and steepness of the line while the y-intercept tells you where the line crosses the y-axis.