In Exercises 45–52, use your answers from Exercises 41–44 and the parametric equations given in Exercises 41–44 to find a set of parametric equations for the conic section or the line.


Line: Passes through (−2,4) and (1,7)

Key Concepts

Parametric Equations

Parametric equations express the coordinates of points on a curve as functions of a variable, often denoted as 't'. For a line, these equations can be derived from two points by defining 't' as a parameter that varies between the two points, allowing for the representation of the line segment in a more flexible way.

Slope of a Line

The slope of a line is a measure of its steepness, calculated as the change in the y-coordinates divided by the change in the x-coordinates between two points. For the points (−2, 4) and (1, 7), the slope can be found using the formula (y2 - y1) / (x2 - x1), which is essential for forming the parametric equations of the line.

Vector Representation

Vector representation involves using a position vector to describe the direction and magnitude of a line. By taking one of the points as a starting point and adding a scaled direction vector (derived from the slope), we can create parametric equations that represent the line in a concise form, facilitating easier calculations and visualizations.