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