To start, we can plot the given point (2, 5) on a coordinate plane. This point means that when x is 2, y is 5.
Next, we use the slope, which is 2, to find other points on the line. A slope of 2 indicates that for every 1 unit you move to the right (increase in x), you move 2 units up (increase in y). Starting from the point (2, 5), let’s find two additional points:
- First point: Move 1 unit to the right from x = 2 to x = 3. From y = 5, move up 2 units to y = 7. So the new point is (3, 7).
- Second point: Again, move from the original point (2, 5) 1 unit to the left to x = 1. From y = 5, move down 2 units to y = 3. So this point is (1, 3).
Having found the points (2, 5), (3, 7), and (1, 3), we can plot these points on the graph and draw a straight line through them.
Now let’s fill out the table with the given x-values:
| x | y |
|---|---|
| 3 | 7 |
| 1 | 3 |
| 2 | 5 |
Finally, to write the equation of the line, we can use the point-slope form of the equation of a line, which is:
y – y1 = m(x – x1)
Using the point (2, 5) and the slope (m = 2), we can substitute these values into the equation:
y – 5 = 2(x – 2)
Now, let’s simplify this equation:
- Distributing the slope: y – 5 = 2x – 4
- Adding 5 to both sides: y = 2x + 1
Therefore, the equation of the line is y = 2x + 1.