Question 710756
The slope-intercept form of the equation of a line is
{{{y=mx+b}}} where the constant {{{m}}} is the slope,
and {{{b}}} is the intercept, the y-coordinate of the point where the line crosses the y-axis.
{{{y = 3x + 1}}} is a line with slope {{{highlight(m=3)}}} that crosses the y-axis at (0,1).
The slope is the "steepness" of the line, the increase in y as x increases by 1.
With a slope of 3, and starting from point (0,1) with x=0, and y=1,
increasing x to x=1, we get to the point with y=1+3=4, point (1,4).
From there, increasing x by 1 to x=2, we get to the point with y=4+3=7, point (2,7).
Parallel lines have the same slope, and (0,0) would be the point where the new line crosses the y-axis,
with y-coordinate=0, so {{{highlight(b=0)}}} and
{{{highlight(y=3x+0)}}} or {{{highlight(y=3x)}}} is your answer.