Determine the equation of the straight line parallel to $y=3x-4$ that passes through the coordinates (1, 5).

The correct option is:
$y=3x+2$

Step 1: Determine the slope of the given line.

The standard slope-intercept form of a straight line is given by:

$y=mx+c$

where $m$ represents the slope and $c$ represents the y-intercept.

Comparing the given line equation $y=3x-4$ with the slope-intercept form, the slope of the given line is:

$m=3$

Step 2: Apply the condition for parallel lines.

Parallel lines have identical slopes. Therefore, the required line parallel to $y=3x-4$ will also have a slope of:

$m=3$

Step 3: Find the equation of the line using the point-slope form.

The point-slope form of a line passing through a point $(x_1,y_1)$ with slope $m$ is:

$y-y_1=m(x-x_1)$

Substitute the slope $m=3$ and the coordinates $(x_1,y_1)=(1,5)$ into the formula:

$y-5=3(x-1)$

Expand the right side of the equation:

$y-5=3x-3$

Add 5 to both sides to solve for $y$:

$y=3x-3+5$

$y=3x+2$

Thus, the equation of the straight line parallel to $y=3x-4$ passing through (1, 5) is:
$y=3x+2$