Final answer:
The equation y=5x is already in slope-intercept form with a slope of 5 and a y-intercept of 0. The point-slope form, given a point like the origin (0,0), is y - 0 = 5(x - 0), which simplifies back to y=5x.
Step-by-step explanation:
The student asked to write an equation for line L in point-slope form and slope-intercept form given the equation y=5x.
The slope-intercept form of an equation is typically written as y=mx+b, where m is the slope and b is the y-intercept. In the case of y=5x, it is already in slope-intercept form with a slope m of 5 and a y-intercept b of 0, because there is no constant term.
For point-slope form, which is given as y - y1 = m(x - x1), we need a specific point through which the line passes. If we choose the origin (0, 0), which lies on this line
since the y-intercept is 0, the point-slope form would be y - 0 = 5(x - 0), which simplifies to y = 5x.
This is a special case where the point-slope form and the slope-intercept form are identical due to the line passing through the origin.