Exercises 143–145 will help you prepare for the material covered in the next section. If (x1,y1) = (-3, 1) and (x2, y2) = (−2, 4), find (y2-y1)/(x2-x1)

Verified step by step guidance

1. Identify the coordinates given: (x₁, y₁) = (-3, 1) and (x₂, y₂) = (-2, 4).
2. Recall the formula for the slope of a line passing through two points: $\frac{y}{}$₂ - y₁x₂ - x₁.
3. Substitute the given values into the formula: $\frac{4\; -\; 1}{-2\; -\; (-3)}$.
4. Simplify the numerator and denominator separately: numerator is $4\; -\; 1$, denominator is $-2\; +\; 3$.
5. Express the slope as a simplified fraction by dividing the simplified numerator by the simplified denominator.

Key Concepts

Slope of a Line

The slope measures the steepness of a line and is calculated as the ratio of the change in y-values to the change in x-values between two points. It is given by (y2 - y1) / (x2 - x1), representing how much y changes for a unit change in x.

Coordinate Points

Coordinate points are ordered pairs (x, y) that locate a point on the Cartesian plane. Understanding how to identify and use these points is essential for calculating distances, slopes, and other geometric properties.

Difference Quotient

The difference quotient is a formula that calculates the average rate of change between two points on a function or line. In this context, it is the slope formula, showing how to find the rate of change between two given points.