Question

The vector v = ai + bj is parallel to the line bx - ay = C. Use this fact to find an equation of the line through P parallel to v. Then draw a sketch of the line including v as a vector starting at the origin.

P( 1,4). v = - i - 4j

Answer 1

The plot diagram is attached for better elaboration of the problem and its solution.

Answer 2

y = 4x

Explanation:

We know that the slopes of parallel lines are equal.

The slope is given by

m = b/a

m = -4/-1

m = 4

the slope intercept form is given by

y = mx + b

y = 4x + b

at point (-1, -4)

-4 = 4(-1) + b

-4 = -4 + b

b = -4 + 4

b = 0

therefore, the equation of the line is

y = 4x + 0

y = 4x