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 - 3x + 4y = 5 into this form
Add 3x to both sides
4y = 3x + 5 ( divide all terms by 4 )
y = [tex]\frac{3}{4}[/tex] x + [tex]\frac{5}{4}[/tex] ← in slope- intercept form
with slope m = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes, thus
y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (2. 1) into the partial equation
1 = [tex]\frac{3}{2}[/tex] + c ⇒ c = - [tex]\frac{1}{2}[/tex]
y = [tex]\frac{3}{4}[/tex] x - [tex]\frac{1}{2}[/tex] ← equation of parallel line
