Write an equation for line l in point-slope form and slope-intercept form.
l is parallel to y=4x.

Point-slope form is just one of many ways of describing a line which states that, given the slope of a line and a point on that line, you have enough information to completely describe that line.

A line is defined by some constant rate of change - its slope. If m is the slope of a line, then we can define m as



Where  is some fixed point and is some other point on the line that we can vary. Here, we know that m = 4, and we're given a fixed point of  to work with, so we have



Multiplying both sides by , we get the equation in point-slope form:



To put the equation in slope-intercept form, we need to find the point where the line hits the y-axis. To do this, we can simply set x = 0:



So, the line hits the y-axis at . Given our slope is 4, and given the general slope-intercept form of a line,



Where m is our slope and b is our y-intercept, the slope-intercept form for our line would be