Question

Which of the following statements are true about this graph? Check all that apply.
The three points do not form a straight line.
The three points form a straight line.
The graph passes through the origin.
The graph does not pass through the origin.
The graph shows a proportional relationship.
The graph does not a show a proportional relationship.On a coordinate plane, points (1, 3), (5, 9), and (7, 12) are plotted.

Answer 1

True:
- The three points form a straight line.
- Slope between (1,3) and (5,9) = (9−3)/(5−1) = 6/4 = 3/2.
Slope between (5,9) and (7,12) = (12−9)/(7−5) = 3/2. Slopes equal ⇒ collinear.
- The graph does not pass through the origin.
- Line through the points: y = (3/2)x + 3/2, y-intercept = 3/2 ≠ 0.
- The graph does not show a proportional relationship.
- A proportional relationship would require the line to pass through the origin; it does not.

The other three statements are false.