What is the equation of the line that passes through (–2, 3) and is parallel to 2x + 3y = 6?

Question

tukitw · Answer

Since the line is parallel, their gradient are the same.
2x + 3y = 6
To find the gradient, solve for y.
3y = -2x + 6
y = -2x / 3 + 2
By comparing this equation with y = mx + c, where m is the gradient, the gradient for the two lines is -2 / 3.
Next, using the point-slope formula, y = m(x - x1) + y1, plug in the corresponding values, with m being the gradient of the line, (x1 , y1) being any coordinate that lies on the line.
So, y = (-2 / 3)(x - -2) + 3, which is from the given (-2 , 3), results in
y = (-2 / 3)(x + 2) + 3 
y = -2x / 3 + 5 / 3.
Finally, rearranging the equation,
3y = -2x + 5
2x + 3y = 5
Thus, the equation of the line that passes through (-2 , 3) is 2x + 3y = 5.