Question

Consider the line passing through the point P, whose position vector is 9 i − 9 j, and parallel to the vector −4 i − 7 j. Find a cartesian equation for the line?

Answer 1

`y = 7/4 x - 99/4`

Explanation:

Being a parallel line means we have a slope. Since it goes through a specific point, we can use point-slope form.

The point is obviously (9, -9) and the slope is
`m = (-7)/(-4) = 7/4`
so we use point-slope form
`y-y_0 = m(x-x_0)`
`y + 9 = 7/4(x-9) rightarrow y = 7/4 x - 99/4`
our final answer.