Answer:
[tex]y=-x-15[/tex]
Step-by-step explanation:
Point-slope formula: [tex]y-y_1=m(x-x_1)[/tex], where [tex](x_1, \ y_1)[/tex] are the coordinates of a point on the line, and [tex]m[/tex] is the slope of the line.
You are given a point that the line you are trying to find passes through, and a slope. The slope is less obvious than the point, but you can find the slope using the given information.
The line perpendicular to y = x + 2 will have the opposite reciprocal slope of this line. The slope of y = x + 2 is 1, so the opposite reciprocal of 1 is:
- [tex]m=-\frac{1}{1} =-1[/tex]
Now that you have both a point and the slope of the line you are trying to find, you can substitute these values into the point-slope formula (Notice: the name of this formula contains both "point" and "slope").
Substitute [tex](-7, \ -8)[/tex] for [tex](x_1,\ y_1)[/tex] and [tex]m=-1[/tex] into the point-slope formula.
- [tex]y-(-8)=-1(x-(-7))[/tex]
Simplify this equation.
Distribute -1 inside the parentheses.
Subtract 8 from both sides of the equation.
This line is in slope-intercept form ([tex]y=mx+b[/tex]), so we are done.
