Answer:
y = x + 5
Step-by-step explanation:
1) First, find the slope of the line [tex]x-y = 4[/tex]. We can do this by setting it up in slope-intercept form, represented by the equation [tex]y = mx + b[/tex]. Whatever [tex]m[/tex] or the coefficient of the x-term is will be the slope. Isolate y in the equation:
[tex]x-y = 4\\-y = -x+4\\y = x -4[/tex]
So, the slope of the given equation is 1. Parallel lines share the same slope, thus the slope of the new line will be 1 as well.
2) Now, use the point-slope formula [tex]y-y_1 = m (x-x_1)[/tex] to write the equation of the line in point-slope form. Substitute values for [tex]m[/tex], [tex]x_1[/tex], and [tex]y_1[/tex] in the formula.
Since [tex]m[/tex] is the slope, substitute 1 for it. Since [tex]x_1[/tex] and [tex]y_1[/tex] represent the x and y values of one point the line passes through, substitute the x and y values of (-6, -1) into those places as well. Then, isolate y in the resulting equation to put the equation in slope-intercept form and find the answer:
[tex]y-(-1) = 1 (x-(-6))\\y + 1 = 1 (x + 6)\\y + 1 = x + 6\\y = x + 5[/tex]
