How do you find the equation of a line that passes through the points (1, 1) and (2, 4)?

To find the equation of a line that passes through two points, we can use the slope-intercept form of a linear equation, which is y = mx + b, where m represents the slope of the line and b represents the y-intercept. Here are the steps to determine the equation:

1. Determine the coordinates of the points: The two points we have are (1, 1) and (2, 4).
2. Calculate the slope (m): The slope can be calculated using the formula:
   
   m = (y₂ – y₁) / (x₂ – x₁)
   
   Substituting the values from our points:
   
   m = (4 – 1) / (2 – 1) = 3 / 1 = 3
3. Use one of the points to find the y-intercept (b): We will use the point (1, 1). Substitute the slope and the coordinates of the point into the slope-intercept formula:
   
   1 = 3(1) + b
   
   Now, solve for b:
   
   1 = 3 + b
   
   b = 1 – 3 = -2
4. Write the equation: Now that we have both the slope (m = 3) and the y-intercept (b = -2), we can write the equation of the line:
   
   y = 3x – 2

In conclusion, the equation of the line that passes through the points (1, 1) and (2, 4) is y = 3x – 2.