Answer (assuming it can be written in slope-intercept format):
[tex]y = -x-6[/tex]
Step-by-step explanation:
1) First, figure out the slope of the line. We know it has to be parallel to the line y = -x -5. That equation is already in slope-intercept format, represented by the equation [tex]y = mx + b[/tex]. The number in place of [tex]m[/tex] represents the slope, thus -1 must be the slope of that line.
All lines that are parallel have the same slope, thus -1 is the slope of the new line as well.
2) Next, use the point-slope formula [tex]y-y_1= m(x-x_1)[/tex] to write the equation of a line. Since [tex]m[/tex] represents the slope, substitute -1 in its place. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of a point the line intersects, substitute the x and y values of (-5, -1) into the formula as well. Then, isolate y to find the following answer and equation:
[tex]y-(-1) = -1(x-(-5))\\y + 1 = -1 (x+5)\\y + 1 = -x -5\\y = -x-6[/tex]
