Question

Input the equation of the given line in standard form.

The line through (1, -4) and parallel to 2x + 3y = 4.

Answer 1

2x + 3y = 4
3y = -2x + 4
y = -2/3x + 4/3
the slope of this line is -2/3. A parallel line will have the same slope.

now we will use y = mx + b
slope(m) = -2/3
(1,-4) x = 1 and y = -4
now we sub and solve for b
-4 = -2/3(1) + b
-4 = -2/3 + b
-4 + 2/3 = b
-12/3 + 2/3 = b
-10/3 = b

now we have :
y = -2/3x - 10/3 -- add 2/3x to both sides
2/3x + y = -10/3 -- multiply by 3
2x + 3y = -10 ===> standard form