Which equation is in point-slope form?

Which equation is in point-slope form?

• A. Ax + By = C
• B. y - y1 = m(x - x1)
• C. a(b + c) = ab + ac
• D. y = mx + b

Answer: (B)

Point-slope form expresses a line using a known point and the slope: y − y1 = m(x − x1). This format directly encodes a point (x1, y1) the line passes through and the slope m. Among the options, the one that fits this pattern is the equation y − y1 = m(x − x1) because it contains both a specific point and the slope. The other forms correspond to different representations or concepts: Ax + By = C is standard form and doesn’t center on a particular point and slope; a(b + c) = ab + ac is the distributive property; y = mx + b is slope-intercept form, which highlights the slope and y-intercept rather than a specific point on the line. If you know a point and the slope, you can start with point-slope form and then convert to other forms as needed, for example by rearranging to y = mx + (y1 − m x1).

Point-slope form expresses a line using a known point and the slope: y − y1 = m(x − x1). This format directly encodes a point (x1, y1) the line passes through and the slope m. Among the options, the one that fits this pattern is the equation y − y1 = m(x − x1) because it contains both a specific point and the slope. The other forms correspond to different representations or concepts: Ax + By = C is standard form and doesn’t center on a particular point and slope; a(b + c) = ab + ac is the distributive property; y = mx + b is slope-intercept form, which highlights the slope and y-intercept rather than a specific point on the line. If you know a point and the slope, you can start with point-slope form and then convert to other forms as needed, for example by rearranging to y = mx + (y1 − m x1).