To find the equation of the line that passes through the points (0, 1) and (2, 5), we first need to determine the slope (m) of the line. The formula to calculate the slope between two points, (x1, y1) and (x2, y2), is:
m = (y2 – y1) / (x2 – x1)
Using the points (0, 1) and (2, 5):
- x1 = 0, y1 = 1
- x2 = 2, y2 = 5
Now, plug the values into the slope formula:
m = (5 – 1) / (2 – 0) = 4 / 2 = 2
Now that we have the slope, we can use the point-slope form of the equation of a line, which is:
y – y1 = m(x – x1)
Substituting (0, 1) for (x1, y1) and 2 for m:
y – 1 = 2(x – 0)
This simplifies to:
y – 1 = 2x
To put this in slope-intercept form (y = mx + b), we add 1 to both sides:
y = 2x + 1
So, the equation of the line that passes through the points (0, 1) and (2, 5) is y = 2x + 1.