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In Exercises 19 and $20,$ find the parametric equation of the line through a parallel to $\mathbf{b}$ . $$\mathbf{a}=\left[\begin{array}{r}{3} \\ {-4}\end{array}\right], \mathbf{b}=\left[\begin{array}{r}{-7} \\ {8}\end{array}\right]$$

$x_{1}=3-7 t$$x_{2}=-4+8 t$

Algebra

Chapter 1

Linear Equations in Linear Algebra

Section 5

Solution Sets of Linear Systems

Introduction to Matrices

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his problem. We're going to find the Parametric equation off the line through when a parallel to vector B. So I'll write down point and vector here. Here's the point. A is three next four on Vector B ISS connective seven and eight. So to do this problem, we just follow the result given me in the textbook, that is, we write down, we write down the point we're passing through as accounts in Victor and we write down the the vector that we that we are required to be parallel to that its neck of 78 as our slope. So that is that is our question for the line. And this line is passing passing through point A, which is three next four and parallel to Vector B, which is a seven and seven and eight Now, bird of war. We can write down the Parametric form, so that is X one because, um, three minus 70 and next to because negative four plus 80 just do the vector addition here. So that is three plus negative seven times the scaler t so that it's a negative 70. So that's our first equation. The second equation the same well, apply the vector additions That has a negative four plus 80. So that is our second question. So this is our parametric form.

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