What is the slope of a line parallel to ##y=3x+5##?

A line parallel to this one would have a slope of 3.

Explanation:

When trying to figure out the slope of a line it's a good idea to put the equation into "slope-intercept" form, which:

##y=mx+b## where m is the slope and b is the y intercept.

In this case, the equation ##y=3x+5## is already in slope intercept form, which means the slope is 3.

Parellel lines have the same slope, so any other line with slope 3 is parallel to this line.

In the graph below, the red line is ##y=3x+5## and the blue line is ##y=3x-2##. As you can see, they are parallel and will never intersect.