Problem 52 - Introductory and Intermediate Algebra for College Students 4th

Question

Describe how to calculate the slope of a line passing through two points.

Step-by-Step Solution

Answer

The slope of a line passing through two points is calculated by the formula \((y_2 - y_1) / (x_2 - x_1)\), which is the change in 'y' divided by the change in 'x' between two points.

Step 1: Understand the Slope Formula

The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula \((y_2 - y_1) / (x_2 - x_1)\). This formula is derived from the definition of 'slope' as the 'change in y' divided by the 'change in x' between two points on a line.

Step 2: Identify the Two Points

Start by identifying the two points. Let's assume that these two points are given as (x1, y1) and (x2, y2).

Step 3: Plug the Coordinates into the Formula

Substitute the coordinates of the two points into the slope formula. Specifically, replace x1, y1, x2, and y2 in the formula \((y_2 - y_1) / (x_2 - x_1)\) with the coordinates of the given points.

Step 4: Perform the Subtractions

Subtract the y1 value from the y2 value for the numerator and the x1 value from the x2 value for the denominator.

Step 5: Unravel the Slope

Finally, divide the difference of y's by the difference of x's to work out the slope.