Which equation represents the two-point form using two points on the line?

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Prepare for the Praxis Middle School Mathematics Exam with quizzes. Study with flashcards and multiple choice questions. Each question provides hints and detailed explanations. Ensure success on your test!

Multiple Choice

Which equation represents the two-point form using two points on the line?

Explanation:
Two points on a line determine its slope, which is (y2 − y1)/(x2 − x1). Once you have that slope, you can write the line in point-slope form through one of the points: y − y1 = m(x − x1). If you substitute m with the two-point slope, you get y − y1 = [(y2 − y1)/(x2 − x1)](x − x1). This is the two-point form, because it uses both given points to define the line. It describes a line that passes through (x1, y1) and (x2, y2) (as long as x2 ≠ x1; a vertical line would be x = x1 instead). The other forms are standard but do not directly encode the two explicit points in the same way.

Two points on a line determine its slope, which is (y2 − y1)/(x2 − x1). Once you have that slope, you can write the line in point-slope form through one of the points: y − y1 = m(x − x1). If you substitute m with the two-point slope, you get y − y1 = [(y2 − y1)/(x2 − x1)](x − x1). This is the two-point form, because it uses both given points to define the line. It describes a line that passes through (x1, y1) and (x2, y2) (as long as x2 ≠ x1; a vertical line would be x = x1 instead). The other forms are standard but do not directly encode the two explicit points in the same way.

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