Answer:
3x + 2y = 13
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
2x - 3y = 6 ( subtract 2x from both sides )
- 3y = - 2x + 6 ( divide all terms by - 3 )
y = [tex]\frac{2}{3}[/tex] x - 2 ← 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 (5, - 1) into the partial equation
- 1 = - [tex]\frac{15}{2}[/tex] + c ⇒ c = - 1 + [tex]\frac{15}{2}[/tex] = [tex]\frac{13}{2}[/tex]
y = - [tex]\frac{3}{2}[/tex] x + [tex]\frac{13}{2}[/tex] ← in slope- intercept form
Multiply through by 2
2y = - 3x + 13 ( add 3x to both sides )
3x + 2y = 13 ← in standard form
