Example 3: Finding the Scalar Equation

Figure 10.2.9

Find a scalar equation for the line in Figure 10.2.9:

X = -4i + j + t(i + 6j).

First method

By Theorem 1, the line has the equation

xd₂ - yd₁ = p₁d₂ - p₂d₁,

6x - y = (-4) · 6 - 1 · 1,

6x - y = -25.

Second method

We convert the vector equation to parametric equations and then eliminate t.

x = -4 + t, y = 1 + 6t,

t = x + 4, y = 1 + 6(x + 4).

y = 25 + 6x.

This is equivalent to the first solution.