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 )
Rearrange x + 5y = 10 into this form
Subtract x from both sides
5y = - x + 10 ( divide all terms by 5 )
y = - [tex]\frac{1}{5}[/tex] x +2 ← in slope- intercept form
with slope m = - [tex]\frac{1}{5}[/tex]
• Parallel lines have equal slopes, hence
y = - [tex]\frac{1}{5}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (1, 3) into the partial equation
3 = - [tex]\frac{1}{5}[/tex] + c ⇒ c = [tex]\frac{16}{5}[/tex]
y = - [tex]\frac{1}{5}[/tex] x + [tex]\frac{16}{5}[/tex] ← equation of parallel line
