Finding the Slope-Intercept Form In Exercises 51-60, write...

Finding the Slope-Intercept Form In Exercises 51-60, write an equation of the line that passes through the points. Use the slope-intercept form (if possible). If not possible, explain why and use the general form. Use a graphing utility to graph the line (if possible). $\left(2, \frac{1}{2}\right),\left(\frac{1}{2}, \frac{5}{4}\right)$

Finding the Slope-Intercept Form In Exercises 51-60, write an equation of the line that passes through the points. Use the slope-intercept form (if possible). If not possible, explain why and use the general form. Use a graphing utility to graph the line (if possible).
$\left(2, \frac{1}{2}\right),\left(\frac{1}{2}, \frac{5}{4}\right)$

Key Concepts

Slope

The slope of a line is a measure of its steepness and is calculated as the ratio of the vertical change (rise) to the horizontal change (run) between two points. This concept is fundamental in determining the orientation and direction of a line in a coordinate plane.

Slope-Intercept Form

The slope-intercept form, expressed as y = mx + b, is a way of writing the equation of a line where m represents the slope and b represents the y-intercept. This form is particularly useful for quickly graphing a line and understanding its behavior.

Point-Slope Form

The point-slope form of a linear equation, given as y - y? = m(x - x?), is used when one point on the line and the slope are known. It provides a direct way to write the equation of a line, which can then be rearranged into other forms, such as the slope-intercept form.

General Form of a Linear Equation

The general form of a linear equation is typically written as Ax + By + C = 0, where A, B, and C are constants. This form is sometimes used when the slope-intercept form is not possible or convenient, offering an alternative way to represent linear relationships.

Graphing Linear Equations

Graphing a linear equation involves plotting the line represented by the equation on a coordinate plane. This process often utilizes a graphing utility or manual plotting techniques to visualize the relationship between x and y.