Questions: Select the correct answer. Which function passes through the points (2,3) and (4,4) ? A. y=2/3 x+2 B. y=x+4 C. y=1/2 x+2 D. y=2 x+3 E. y=2 x+1/2

Solution Steps

To determine which function passes through the given points, we need to check which of the provided equations satisfy both points. This involves substituting the x-values of the points into each equation and checking if the resulting y-values match the given points.

We are given two points: \( (2, 3) \) and \( (4, 4) \). We need to find which of the provided functions passes through both of these points.

We will evaluate each function to see if it satisfies both points. The functions provided are:

• A: \( y = \frac{2}{3} x + 2 \)
• B: \( y = x + 4 \)
• C: \( y = \frac{1}{2} x + 2 \)
• D: \( y = 2 x + 3 \)
• E: \( y = 2 x + \frac{1}{2} \)

After evaluating the functions, we find that function C, \( y = \frac{1}{2} x + 2 \), passes through both points:

• For \( x = 2 \): \( y = \frac{1}{2}(2) + 2 = 1 + 2 = 3 \)
• For \( x = 4 \): \( y = \frac{1}{2}(4) + 2 = 2 + 2 = 4 \)

Final Answer