Final answer:
To find the value of y on a line with a slope of 2 that passes through (1,2) and (3,y), calculate the run (3 - 1), multiply it by the slope (2 * 2), and add the result to the initial y-value (2 + 4), which gives y=6.
Step-by-step explanation:
How to Find the Y-Coordinate Without Using the Equation y=mx+b
The question asks to find the value of y when a line with a slope of 2 passes through the points (1,2) and (3,y). Since the slope of a line represents the rate of change of y with respect to x, it is defined as the rise over the run. In this case, for every increase of 1 in the x-coordinate, the y-coordinate increases by 2, as indicated by the slope of 2.
To find the value of y, we can use the two points given. We know the line passes through point (1,2) and we need to find the corresponding y for the point (3,y). We can use the concept of slope as follows:
- Calculate the difference in x-coordinates (the run), which is 3 - 1 = 2.
- Multiply the run by the slope to find the change in y (the rise), which is 2 * 2 = 4.
- Add this change to the initial y-value of the first point to find the final y. Thus, 2 + 4 = 6.
Therefore, the value of y that corresponds to the x-coordinate of 3 is 6. The coordinates of the second point are (3,6).