Answer:
y = x + 3
Step-by-step explanation:
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = - x - 6 ← is in slope- intercept form
with slope m = - 1
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{-1}[/tex] = 1, thus
y = x + c ← is the partial equation
To find c substitute (1, 4) into the partial equation
4 = 1 + c ⇒ c = 4 - 1 = 3
y = x + 3 ← equation of line
