The y-intercept of the line 2

To find the equation of a line with a given y-intercept and slope, we can use the slope-intercept form of a line, which is given by:

\[ y = mx + b \]

where \( m \) is the slope and \( b \) is the y-intercept.

From your information:

• The y-intercept (\( b \)) is 2.
• The slope (\( m \)) is \( \frac{1}{4} \).

Substituting these values into the slope-intercept formula gives:

\[ y = \frac{1}{4}x + 2 \]

Now, let's match this with the options provided:

A. \( y = \frac{4}{1} x + 2 \) (which simplifies to \( y = 4x + 2 \), incorrect)

B. \( y = -\frac{1}{2} x + 4 \) (incorrect slope and y-intercept)

C. \( y = \frac{1}{4} x + 2 \) (correct)

D. \( y = 2x + 4 \) (incorrect slope and y-intercept)

The correct answer is:

C. \( y = \frac{1}{4} x + 2 \)