Problem:

Write parametric equations of a line through (7,5) with slope of 3. Graph the line using your equations.

Let

denote the position vector of a point P on the line and let

denote the position vector of point Q.

Using algebra, the line

is parallel to the vector

Hence, the vector parametric equation is

The resulting scalar parametric equations are

Let (X0, Y0) = (7, 5) and using the slope of 3, let (X1, Y1) = (8, 8). So

and

Using these parametric equations, the graph of the line is

The graph of the line

shown in blue is on the path of the parametric equations that were graphed previously.

Return to Class Page