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Write an equation for line L in point-slope form and slope-intercept form y=5x

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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.

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