What is the equation of the line passing through (3, 4) with slope 2?

The equation of the line passing through (3, 4) with slope 2 is \( y = 2x - 2 \).

To find the equation of a line, we use the slope-intercept form, which is \( y = mx + c \), where \( m \) is the slope and \( c \) is the y-intercept. Given the slope \( m = 2 \) and a point on the line (3, 4), we can substitute these values into the equation to find \( c \).

First, substitute the slope \( m = 2 \) into the equation:
\[ y = 2x + c \]

Next, use the point (3, 4) to find \( c \). Substitute \( x = 3 \) and \( y = 4 \) into the equation:
\[ 4 = 2(3) + c \]

Simplify the equation:
\[ 4 = 6 + c \]

To find \( c \), subtract 6 from both sides:
\[ c = 4 - 6 \]
\[ c = -2 \]

Now, substitute \( c = -2 \) back into the slope-intercept form:
\[ y = 2x - 2 \]

So, the equation of the line passing through the point (3, 4) with a slope of 2 is \( y = 2x - 2 \). This equation tells us that for every unit increase in \( x \), \( y \) increases by 2 units, and the line crosses the y-axis at -2.