To find the equation of a line that passes through the points (0, 1) and (2, 3), we’ll first determine the slope (m) of the line using the formula:
m = (y2 – y1) / (x2 – x1)
Here, we can take (x1, y1) as (0, 1) and (x2, y2) as (2, 3). Plugging these values into the slope formula gives us:
m = (3 – 1) / (2 – 0) = 2 / 2 = 1
Now that we have the slope, we can use the point-slope form of the equation of a line:
y – y1 = m(x – x1)
Substituting in the slope (m = 1) and one of our points, let’s use (0, 1):
y – 1 = 1(x – 0)
This simplifies to:
y – 1 = x
Finally, rearranging this equation gives us the slope-intercept form:
y = x + 1
Thus, the equation of the line that passes through the points (0, 1) and (2, 3) is y = x + 1.