Identify Points on the Line: y = 1/2x + 3/4

Through which points does the following function pass?

$y=\frac{1}{2}x+\frac{3}{4}$

To solve this problem, we need to check each given point to determine if it lies on the line represented by the equation $y = \frac{1}{2}x + \frac{3}{4}$.

• Check Point (1): $(1, \frac{4}{5})$
  Substitute $x = 1$ into the function:
  $y = \frac{1}{2}(1) + \frac{3}{4} = \frac{1}{2} + \frac{3}{4} = \frac{2}{4} + \frac{3}{4} = \frac{5}{4} \neq \frac{4}{5}$.
  The point does not lie on the line.

• Check Point (2): $(1, 2\frac{1}{4})$
  Substitute $x = 1$:
  $y = \frac{1}{2}(1) + \frac{3}{4} = \frac{5}{4} \neq 2\frac{1}{4}$.
  The point does not lie on the line.

• Check Point (3): $(3, 2\frac{1}{4})$
  Substitute $x = 3$:
  $y = \frac{1}{2}(3) + \frac{3}{4} = \frac{3}{2} + \frac{3}{4} = \frac{6}{4} + \frac{3}{4} = \frac{9}{4} = 2\frac{1}{4}$.
  The point lies on the line.

• Check Point (4): $(4, 2\frac{3}{4})$
  Substitute $x = 4$:
  $y = \frac{1}{2}(4) + \frac{3}{4} = 2 + \frac{3}{4} = \frac{8}{4} + \frac{3}{4} = \frac{11}{4} = 2\frac{3}{4}$.
  The point lies on the line.

The points $(3, 2\frac{1}{4})$ and $(4, 2\frac{3}{4})$ satisfy the equation, indicating that these points are on the line.
Therefore, the solution is Answers C and D are correct.