For this case we have that by definition, the equation of the line in the slope-intersection form is given by:
[tex]y = mx + b[/tex]
Where:
m: It's the slope
b: It is the cut-off point with the y axis
We have the following equation:
[tex]6x + 5y = -5\\5y = -6x-5\\y = - \frac {6} {5} x- \frac {5} {5}\\y = - \frac {6} {5} -1[/tex]
Thus, the slope is: [tex]m = - \frac {6} {5}[/tex]
By definition, if two lines are parallel then their slopes are equal.
Thus, a line parallel to the given line will have a slope: [tex]m = - \frac {6} {5}.[/tex]Therefore, the equation will be of the form:
[tex]y = - \frac {6} {5} x + b[/tex]
We substitute the given point and find "b":
[tex]-4 = - \frac {6} {5} (5) + b\\-4 = -6 + b\\-4 + 6 = b\\b = 2[/tex]
Finally, the equation is:
[tex]y = - \frac {6} {5} x + 2[/tex]
Answer:
[tex]y = - \frac {6} {5} x + 2[/tex]
