Answer:
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 [tex]\left(x_{1}, y_{1}\right)[/tex] and parallel to the line with slope “m” is given as
[tex]y-y_{1}=m\left(x-x_{1}\right)[/tex] ---- equation 1
Where “m” is the slope of the line. [tex]x_{1}[/tex] and [tex]y_{1}[/tex] 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 [tex]x_{1}=1[/tex] and [tex]y_{1}=-5[/tex]
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
