Final answer:
The equation of the line that is parallel to the line 2x - 5y = 35 and passes through the point (5,-2) is y = (2/3)x - 8/3.
Step-by-step explanation:
To find the equation of a line that is parallel to the line 2x - 5y = 35 and passes through the point (5, -2), we need to use the fact that parallel lines have the same slope. The slope of the given line is found by rearranging the equation to the slope-intercept form y = mx + b, where m is the slope. In this case, the slope is 2/3. So, the equation of the line parallel to the given line is y = (2/3)x + b. To find the y-intercept, plug in the coordinates of the point (5, -2) into the equation and solve for b.
Substituting x = 5 and y = -2 in the equation, we get -2 = (2/3)(5) + b. Simplifying this equation, we have -2 = 10/3 + b. Subtracting 10/3 from both sides, we get -8/3 = b. Therefore, the equation of the line parallel to the given line and passing through the point (5, -2) is y = (2/3)x - 8/3.