Answer:
3x + 2y = 14
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 - 3y = 5 into this form by subtracting 2x from both sides
- 3y = - 2x + 5 ( divide all terms by - 3 )
y = [tex]\frac{2}{3}[/tex] x - [tex]\frac{5}{3}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{2}{3}[/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{2}{3} }[/tex] = - [tex]\frac{3}{2}[/tex] , thus
y = - [tex]\frac{3}{2}[/tex] x + c ← is the partial equation
To find c substitute (4, 1) into the partial equation
1 = - 6 + c ⇒ c = 1 + 6 = 7
y = - [tex]\frac{3}{2}[/tex] x + 7 ← in slope- intercept form
Multiply through by 2
2y = - 3x + 14 ( add 3x to both sides )
3x + 2y = 14 ← in standard form
