Answer:
see explanation
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 = - [tex]\frac{3}{4}[/tex] x + 3 ← is in slope- intercept form
with slope m = - [tex]\frac{3}{4}[/tex]
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}{-\frac{3}{4} }[/tex] = [tex]\frac{4}{3}[/tex] , then
y = [tex]\frac{4}{3}[/tex] x + c ← is the partial equation
To find c substitute (3, 7 ) into the partial equation
7 = 4 + c ⇒ c = 7 - 4 = 3
y = [tex]\frac{4}{3}[/tex] x + 3 ← in slope- intercept form
The equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
Here m = [tex]\frac{4}{3}[/tex] and (a, b ) = (3, 7 ) , then
y - 7 = [tex]\frac{4}{3}[/tex] (x - 3) ← in point- slope form
