How do you write an equation of a translated line given the equation of the original line and both the translated and original lines on a graph??

Thanks in advance!!

2x+3x=?

You will need the equation of the original line, and a way to know where the translated line will go.

The destination is usually a point through which the translated line will pass, or the (perpendicular) distance between the two lines.
See if you can figure out the information and post it in a more concrete form.
Different data require different methods.

To write an equation of a translated line, you need three key pieces of information: the equation of the original line, the direction and magnitude of the translation, and the coordinates of a point on the translated line.

Here's a step-by-step process to write the equation:

1. Start with the equation of the original line. It should be in the form y = mx + b, where m represents the slope and b represents the y-intercept.

2. Identify the direction and magnitude of the translation. Is the line shifted vertically, horizontally, or a combination of both? Determine if the line is moved up or down, left or right, or a combination of both.

3. Adjust the equation based on the direction and magnitude of the translation:
- Vertical Translation: If the line is shifted up or down, add or subtract a constant value to the original equation. If the line is shifted up by h units, add +h to the original equation; if shifted down, subtract h.
- Horizontal Translation: If the line is shifted left or right, adjust the x-values in the original equation by adding or subtracting a constant value. If the line is shifted right by k units, subtract -k from the x-values; if shifted left, add k.
- Combined Translation: If the line is shifted both vertically and horizontally, perform both adjustments simultaneously (follow the same steps as above).

4. Determine the coordinates of a known point on the translated line. This point should be visible on the graph of the translated line. If you only have the original line and the translated line on the graph, find a coordinate point common to both lines.

5. Substitute the coordinates of the known point into the adjusted equation. Replace x and y in the equation with the x-coordinate and y-coordinate of the known point.

6. Simplify and rearrange the equation if necessary. Use algebraic techniques to simplify the equation and express it in the standard form (if applicable).

Following these steps will allow you to write an equation of a translated line.