In the point-slope form y - y1 = m(x - x1), what does (x1, y1) represent?

In the point-slope form y - y1 = m(x - x1), what does (x1, y1) represent?

• A. (x1, y1) is a point on the line
• B. The slope
• C. The x-intercept
• D. The y-intercept

Answer: (A)

In point-slope form, the pair (x1, y1) is a point on the line. It serves as a fixed point that the line passes through, and the slope m tells you how steeply the line rises or falls from that point. If you plug x = x1 into the equation y − y1 = m(x − x1), you get y = y1, which confirms the line goes through (x1, y1). The x-intercept and y-intercept are specific points where the line crosses the axes and are not generally the same as (x1, y1). So this pair is best understood as a point on the line used to define its position and direction.

In point-slope form, the pair (x1, y1) is a point on the line. It serves as a fixed point that the line passes through, and the slope m tells you how steeply the line rises or falls from that point. If you plug x = x1 into the equation y − y1 = m(x − x1), you get y = y1, which confirms the line goes through (x1, y1). The x-intercept and y-intercept are specific points where the line crosses the axes and are not generally the same as (x1, y1). So this pair is best understood as a point on the line used to define its position and direction.