Answer:
y = [tex]\frac{1}{4}[/tex] x + 6
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 )
given
4x + y = 7 ( subtract 4x from both sides )
y = - 4x + 7 ← in slope- intercept form
with slope m = - 4
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}{-4}[/tex] = [tex]\frac{1}{4}[/tex] , then
y = [tex]\frac{1}{4}[/tex] x + c ← is the partial equation of the perpendicular line
to find c substitute )- 4, 5 ) into the partial equation
5 = - 1 + c ⇒ c = 5 + 1 = 6
y = [tex]\frac{1}{4}[/tex] x + 6 ← equation of perpendicular line
