Given:
The line parallel to y = −x that passes through (7, 2.5).
To find:
The slope intercept form of the given line.
Solution:
Slope intercept form of the line is
[tex]y=mx+b[/tex]
where, m is slope and b is y-intercept.
On comparing y = −x with slope intercept form, we get
[tex]m=-1[/tex]
So, slope of y=-x is -1.
Slope of parallel lines are same. Thus, slope of required line is -1.
Required line passes through (7,2.5) with slope -1. So, the equation of line is
[tex]y-y_1=m(x-x_1)[/tex]
[tex]y-2.5=-1(x-7)[/tex]
[tex]y-2.5=-x+7[/tex]
Add 2.5 on both sides.
[tex]y-2.5+2.5=-x+7+2.5[/tex]
[tex]y=-x+9.5[/tex]
Therefore, the equation of the line that passes through (7, 2.5) is [tex]y=-x+9.5[/tex].
