find tha equation of a line which is parallel to the line 2x-3y=8 whose y-intercept is 5 units

To find the equation of a line parallel to the line 2x-3y=8, we need to consider two main elements: the slope and the y-intercept.

1. Finding the slope:
The given equation is in the form of Ax + By = C, where A = 2 and B = -3. To find the slope, we need to rearrange the equation to the slope-intercept form (y = mx + b), where m represents the slope.

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

From this equation, we can see that the slope is 2/3.

2. Parallel lines have the same slope, which means our parallel line will also have a slope of 2/3.

3. Finding the y-intercept:
We are told that the y-intercept is 5 units. The y-intercept is the point where the line crosses the y-axis, which occurs when x = 0. Therefore, the y-intercept is the point (0, 5).

4. Using the slope-intercept form:
Using the slope (m = 2/3) and the y-intercept (0, 5), we can write the equation of the line in the slope-intercept form as follows:

y = mx + b
y = (2/3)x + 5

Thus, the equation of the line parallel to 2x - 3y = 8 with a y-intercept of 5 units is y = (2/3)x + 5.

you want the line through (0,5) that has slope 2/3. So,

y-5 = 2/3 x