y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex]
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y-intercept )
y = 4x + 5 is in this form with slope m - 4
Given the slope of a line m, then the slope ([tex]m_{2}[/tex]) of a line perpendicular to it is
[tex]m_{2}[/tex] = - (1 / m ) = - [tex]\frac{1}{4}[/tex]
y = - [tex]\frac{1}{4}[/tex] x + c is the partial equation of the perpendicular line
to find c, substitute ( 2, 7 ) into the partial equation
7 = - [tex]\frac{1}{2}[/tex] + c ⇒ c = [tex]\frac{15}{2}[/tex]
y = - [tex]\frac{1}{4}[/tex] x + [tex]\frac{15}{2}[/tex] ← equation of perp. line
