y = -x - 4 is the equation of a line in slope-intercept form, that is perpendicular to -x + y = 1 and goes through (1, -5)
Solution:
Given that we have to write the equation of a line in slope-intercept form, that is perpendicular to -x + y = 1 and goes through (1, -5)
The equation of line in slope intercept form is given as:
y = mx + c ------ eqn 1
Where, "m" is the slope of line and "c" is the y intercept
Given equation of line is:
-x + y = 1
Rearrange into slope intercept form
y = x + 1
On comparing the above equation with eqn 1,
m = 1
We know that,
Product of slope of line and slope of line perpendicular to given line is equal to -1
Therefore,
Slope of line perpendicular to given line = -1
Now we have to find the equation of line with slope -1 and passing through (1, -5)
Substitute m = -1 and (x, y) = (1, -5) in eqn 1
-5 = -1(1) + c
c - 1 = -5
c = -5 + 1
c = -4
Substitute c = -4 and m = -1 in eqn 1
y = -x - 4
Thus the equation of line is found