Answer:
3x - y = 6
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
x + 3y = 21 ( subtract x from both sides )
3y = - x + 21 ( divide all terms by 3 )
y = - [tex]\frac{1}{3}[/tex] x + 7 ← in slope- intercept form
with slope m = - [tex]\frac{1}{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{1}{3} }[/tex] = 3 , thus
y = 3x + c ← is the partial equation
To find c , substitute (1, - 3) into the partial equation
- 3 = 3 + c ⇒ c = - 3 - 3 = - 6
y = 3x - 6 ← in slope- intercept form
subtract y from both sides
0 = 3x - y - 6 ( add 6 to both sides )
6 = 3x - y , that is
3x - y = 6 ← in standard form
