Question

Write the point-slope form of the line that passes through (6,1) and is parallel to a line with a slope of -3 include all of your work in your final answer.

Answer 1

The point-slope form of the line that passes through (6,1) and is parallel to a line with a slope of -3 is 3x + y – 19 = 0

Solution:

The point slope form of the line that passes through the points
`\left(x_(1) y_(1)\right)` and parallel to the line with slope “m” is given as

`y - y_(1) = m\left(x - x_(1)\right)` --- eqn 1

Where “m” is the slope of the line.
`x_(1) \text { and } y_(1)`are the points that passes through the line.

From question, given that slope “m” = -3

Given that the line passes through the points (6,1).Hence we get
`x_(1) = 6 ; y_(1) = 1`

By substituting the values in eqn 1, we get the point slope form of the line which is parallel to the line having slope -3 can be found out.

y – 1 = -3(x – 6)

y – 1 = -3x +18

On rearranging the terms, we get

3x + y -1 – 18 = 0

3x + y – 19 = 0

Hence the point slope form of given line is 3x + y – 19 = 0