Final answer:
To translate the line 3x + 5y = 10 four units up, you add 4 to the y-coordinate, resulting in the new equation 3x + 5y = -10.
Step-by-step explanation:
The question is asking to write the equation of the line that has been translated 4 units up from its original position. The original equation is 3x + 5y = 10. When a line is moved vertically up or down, its slope remains the same, but its y-intercept changes. To translate the line 4 units up, you would add 4 to the y-coordinate of every point on the line. This means the new equation will be 3x + 5y = 10 - 20 (because 5y is the same as y multiplied by 5, and to keep the equation balanced, we need to subtract 5 times the number of units we are moving up, which is 4). Therefore, the new equation will be 3x + 5y = -10.