Answer:
y = - [tex]\frac{1}{3}[/tex] x + 5
Step-by-step explanation:
The equation of a line in slope - intercept form is
y = mx + b ( m is the slope and b the y- intercept )
Given
x + 3y = 24 ( subtract x from both sides )
3y = - x + 24 ( divide all terms by 3 )
y = - [tex]\frac{1}{3}[/tex] x + 8 ← in slope- intercept form
with slope m = - [tex]\frac{1}{3}[/tex]
Parallel lines have equal slopes , thus
y = - [tex]\frac{1}{3}[/tex] x + b ← is the partial equation
To find c substitute (6, 3) into the partial equation
3 = - 2 + b ⇒ b = 3 + 2 = 5
y = - [tex]\frac{1}{3}[/tex] x + 5 ← equation of parallel line
