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 = 7 into this form
Subtract 3x from both sides
- 4y = - 3x + 7 ( divide all terms by - 4 )
y = [tex]\frac{3}{4}[/tex] x - [tex]\frac{7}{4}[/tex] ← in slope- intercept form
with slope = [tex]\frac{3}{4}[/tex]
• Parallel lines have equal slopes, hence
y = [tex]\frac{3}{4}[/tex] x + c ← is the partial equation of the parallel line
To find c substitute (- 4, - 2) into the partial equation
- 2 = - 3 + c ⇒ c = - 2 + 3 = 1
y = [tex]\frac{3}{4}[/tex] x + 1 ← in slope- intercept form
Multiply all terms by 4
4y = 3x + 4 ( subtract 4 from both sides )
4y - 4 = 3x ( subtract 4y from both sides )
- 4 = 3x - 4y, that is
3x - 4y = - 4 ← in standard form
