Find the equation of a line passing through the point(2, 3) and parallel to the line 2x - 3y + 8 = 0.

Solution:

The slope of the line 2x - 3y + 8 = 0 can be derived from the equation itself by rewriting it in the form y = mx + c

y = (2/3)x + (8/3)

Hence the slope of the equation is 2/3.

To find the equation of the line passing through the point (x, y) and slope m is given as: (y - y₁) = m(x - x₁)

Since this line is parallel to the equation 2x - 3y + 8 = 0 its slope is:

m = 2/3

And since this line passes through (x₁ = 2; y₁ = 3) the equation of the line can be derived as follows:

(y - 3) = (2/3)(x - 2)

3y - 9 = 2x - 4

2x - 3y + 5 = 0

Therefore, the equation of line is 2x - 3y + 5 = 0.

Find the equation of a line passing through the point(2, 3) and parallel to the line 2x - 3y + 8 = 0.

Summary:

The equation of the line passing through (2, 3) and parallel to the line 2x - 3y + 8 = 0 is 2x - 3y + 5 = 0.