How do you write the equation of a line passing through (3, 2) with slope 5?

The equation of the line passing through (3, 2) with a slope of 5 is \( y = 5x - 13 \).

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 \( m = 5 \) and a point on the line (3, 2), we can substitute these values into the equation to find \( c \).

First, substitute the slope and the coordinates of the point into the slope-intercept form:
\[ 2 = 5(3) + c \]

Next, solve for \( c \):
\[ 2 = 15 + c \]
\[ c = 2 - 15 \]
\[ c = -13 \]

Now that we have the slope \( m = 5 \) and the y-intercept \( c = -13 \), we can write the equation of the line:
\[ y = 5x - 13 \]

This equation tells us that for any value of \( x \), you can find the corresponding \( y \) value by multiplying \( x \) by 5 and then subtracting 13. For example, if \( x = 0 \), then \( y = -13 \), and if \( x = 1 \), then \( y = -8 \). This linear relationship is consistent with the given slope and the point through which the line passes.