The equation of a line in the slope intercept form is expressed as
y = mx + c
where
m = slope
c = y intercept
The given equation is expressed as
5x + 2y = 14
By rearranging the given equation so that it looks like the slope intercept equation, it becomes
2y = 14 - 5x
2y - 5x + 14
Dividing both sides of the equation by 2,
y = - 5x/2 + 7
By comparing with the slope intercept equation, slope = - 5/2
Recall, if two lines are parallel, it means that they have the same slope. Thus, the slope of the parallel line passing through the point (- 2, - 3) is - 5/2
We would find the y intercept by substituting x = - 2, y = - 3 and m = - 5/2 into the slope intercept equation. We have
- 3 = - 2 * - 5/2 + c = 5 + c
c = - 3 - 5 = - 8
By substituting m = - 5/2 and c = - 8 into the slope intercept equation, the equation of the paralle line is
y = - 5x/2 - 8