Question

write an equation for a line containing (1,4) and parallel to the line 3y-4x=12.

Answer 1

Given line 3y - 4x  = 12

Add 4x  to each side.

3y  = 4x + 12

Divide each side by 3.

y = 4x/3 + 4

Compare it to slope intercept form of a line y = mx + b.

Slope = 4/3.

We know that parallel lines have equal slope.

Parallel line through ( 1, 4).

Equation of a line in  point slope form is 

Cross multiplication.

3y  -12 = 4x - 4

Add 12 to each side.

3y = 4x + 8

y = 4x /3 + 8/3

Required line equation y = 4x /3 + 8/3.