To find the equation of the line that passes through the two given points, (0, 1) and (2, 3), we can follow these steps:
Step 1: Determine the Slope
The slope (m) of a line that passes through two points, (x1, y1) and (x2, y2), can be calculated using the formula:
m = (y2 – y1) / (x2 – x1)
For our points, (0, 1) and (2, 3):
- (x1, y1) = (0, 1)
- (x2, y2) = (2, 3)
Plugging in the values:
m = (3 – 1) / (2 – 0) = 2 / 2 = 1
Step 2: Use the Point-Slope Form of the Line
With the slope found, we can use the point-slope form of the equation of a line:
y – y1 = m(x – x1)
Substituting m = 1 and using the point (0, 1):
y – 1 = 1(x – 0)
y – 1 = x
Step 3: Rearranging to Slope-Intercept Form
Now let’s rearrange the equation to get it into slope-intercept form (y = mx + b):
y = x + 1
Conclusion
The equation of the line that passes through the points (0, 1) and (2, 3) is: