How do you write the equation of a line that passes through the points (2, 2) and (3, 4)?

To find the equation of the line that passes through the two given points, (2, 2) and (3, 4), we can use the following steps:

1. Determine the slope (m)
   The slope of a line that passes through two points

   (x_1, y_1) and (x_2, y_2)

   is given by the formula:
   
   m = (y_2 - y_1) / (x_2 - x_1)
   
   For our points (2, 2) and (3, 4):
   
   m = (4 - 2) / (3 - 2) = 2 / 1 = 2

2. Use point-slope form of a line
   The point-slope form of the equation of a line is:
   
   y - y_1 = m(x - x_1)
   
   You can use either of the given points for (x_1, y_1). Let’s use (2, 2):
   
   y - 2 = 2(x - 2)
3. Simplify to slope-intercept form
   Now, we will simplify this equation to get it into the slope-intercept form (y = mx + b):
   
   y - 2 = 2x - 4

y = 2x - 2

So, the equation of the line that passes through the points (2, 2) and (3, 4) is:

y = 2x - 2

This equation expresses a linear relationship between x and y, with a slope of 2 and a y-intercept of -2.