Answer:
y = 2x + 1
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 )
rearrange 2x + 4y = - 6 into this form
subtract 2x from both sides
4y = - 2x - 6 ( divide all terms by 4 )
y = - [tex]\frac{1}{2}[/tex] x - [tex]\frac{3}{2}[/tex] ← in slope-intercept form
with slope m = - [tex]\frac{1}{2}[/tex]
the slope of the perpendicular line is the negative reciprocal of m
[tex]m_{perpendicular}[/tex] = 2
y = 2x + c ← is the partial equation
to find c substitute (2, 5) into the partial equation
5 = 4 + c ⇒ c = 5 - 4 = 1
y = 2x + 1 ← equation of perpendicular line
