Question

write the point-slope form of the line that passes through (1,-5) and is parallel to a line with a slope of 1. include all your work in your final answer.

Answer 1

The point-slope form of the line that passes through (1,-5) and is parallel to a line with a slope of 1 is y + 5 = x – 1

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)` ---- equation 1

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

From question, given that slope “m” = 1

Given that the line passes through the points (1,-5). Hence we get
`x_(1)=1` and
`y_(1)=-5`

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

y – (-5) = 1(x – 1)

y + 5 = x – 1

hence the point slope form of given line is y + 5 = x – 1