An equation which is parallel to 4x - 6y = -36 passing through points (2, 3) is y = 2x/3 + 5/9.
Parallel lines can be defined as two (2) lines that are always the same (equal) distance apart and never meet.
In Geometry, two (2) lines are considered to be parallel if their slopes are the same (equal) and they've different y-intercepts.
This ultimately implies that, two (2) lines are parallel under the following conditions:
m₁ = m₂
Note: m is the slope.
Simplifying the equation, we have:
4x - 6y = -36
6y = 4x + 36
Dividing both sides by 6, we have:
y = 2x/3 + 6
m₁ = m₂ = 2/3.
Mathematically, the standard form of the equation of a straight line is given by;
y - y₁ = m(x - x₁)
At point (2, 3), we have:
y - 3 = 2/3(x - 2)
y - 3 = 2/3(x - 2)
y - 3 = 2x/3 - 4/3
y = 2x/3 - 4/3 + 3
y = 2x/3 + 5/9
Read more on slope of parallel lines here: brainly.com/question/28427398
#SPJ1
