Step-by-step explanation:
The equation of the given line is 3x - 4y = 1
A line parallel to the given line will have slope that is the same as this one.
The equation of a straight line is expressed as;
y = mx + c
y and x are the coordinates
m is the slope
c is the y-intercept
Now, we write the given line in the slope - intercept form;
3x - 4y = 1
-4y = -3x + 1
Divide through by -4
[tex]\frac{-4y}{-4}[/tex] = [tex]\frac{-3x}{-4}[/tex] + [tex]\frac{1}{-4}[/tex]
y = [tex]\frac{3}{4} x[/tex] - [tex]\frac{1}{4}[/tex]
The slope of this line is [tex]\frac{3}{4}[/tex]
Any line with the slope [tex]\frac{3}{4}[/tex] will be parallel to the given line.
