Which equation represents the line with slope m passing through the point (x1, y1)?

Which equation represents the line with slope m passing through the point (x1, y1)?

• A. y - y1 = m(x - x1)
• B. y = mx + b
• C. y - y1 = (x - x1)/m
• D. y1 - y = m(x - x1)

Answer: (A)

To describe a line with a given slope passing through a specific point, use the point-slope form. The equation y − y1 = m(x − x1) directly ties the slope to the point (x1, y1): the rise over run between any point (x, y) on the line and (x1, y1) is always m. If you set x = x1, you get y = y1, so the line indeed passes through the given point, and rearranging to slope-intercept form gives y = mx + (y1 − m x1), confirming the slope is m. The other forms either introduce a reciprocal slope (y − y1 = (x − x1)/m), reverse signs (y1 − y = m(x − x1) implies slope −m), or express a general line with slope m but do not single out the specific line through (x1, y1) without extra information.

To describe a line with a given slope passing through a specific point, use the point-slope form. The equation y − y1 = m(x − x1) directly ties the slope to the point (x1, y1): the rise over run between any point (x, y) on the line and (x1, y1) is always m. If you set x = x1, you get y = y1, so the line indeed passes through the given point, and rearranging to slope-intercept form gives y = mx + (y1 − m x1), confirming the slope is m. The other forms either introduce a reciprocal slope (y − y1 = (x − x1)/m), reverse signs (y1 − y = m(x − x1) implies slope −m), or express a general line with slope m but do not single out the specific line through (x1, y1) without extra information.