Determining the Slope of a Line Given Two Points

In high school mathematics, understanding the concept of slope is crucial for working with linear equations and graphing lines in the coordinate plane. The slope of a line represents the rate of change between two points on that line, and it provides valuable information about the line's direction and steepness.

To determine the slope of a line containing the points Y and Z, we can use the slope formula:

Slope = (y₂ - y₁) / (x₂ - x₁)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two given points.

Let's consider the following options and determine the correct slope of the line containing points Y and Z:

a. Slope = -0.5 b. Slope = -1 c. Slope = -2 d. Slope = -4

To solve this problem, we need to apply the slope formula and calculate the slope based on the given information.

Given information:

• The line contains the points Y and Z.

Step 1: Identify the coordinates of the two points. Let's assume the coordinates of point Y are (x₁, y₁) and the coordinates of point Z are (x₂, y₂).

Step 2: Apply the slope formula. Slope = (y₂ - y₁) / (x₂ - x₁)

Step 3: Evaluate the slope based on the given options. a. Slope = -0.5 b. Slope = -1 c. Slope = -2 d. Slope = -4

To determine the correct slope, we need to compare the calculated slope using the formula with the given options.

The correct answer is the option that matches the slope calculated using the formula.

By working through this problem, students will develop a deeper understanding of the concept of slope and how to apply the slope formula to determine the slope of a line given two points.