Answer :
The Equation of a Line
The slope-intercept of the line is:
y = mx + b
Where m is the slope and m is the y-intercept of the line.
The point-slope form of the line is:
y = m(x - h) + k
Where (h, k) is a point of the line.
We know our line is parallel to:
6x + y = 6
Parallel lines have the same slope. The slope of this line can be found by solving for y:
[tex]y=-6x+6[/tex]The slope of the given line and the slope of our required line is m = -6.
We use the point-slope form with the slope m = -6 and the point (2, -5):
[tex]\begin{gathered} y=-6(x-2)-5 \\ \text{Operating:} \\ y=-6x+12-5 \\ y=-6x+7 \end{gathered}[/tex]The required equation of the line is:
y = -6x + 7