Find Intercepts by Setting the Other Coordinate to Zero

Supplied materials

• Paper or a browser scratch area; a calculator is optional unless rounding is requested.
• Supplied teaching case: Find both intercepts of 2x+3y=12. Candidate answers: (A) (12,0) and (0,12) (B) (2,0) and (0,3) (C) (4,0) and (0,6) (D) (6,0) and (0,4).
• Independent check inputs: Find both intercepts of 2x+3y=18. Candidate answers: (A) (18,0) and (0,18) (B) (2,0) and (0,3) (C) (6,0) and (0,9) (D) (9,0) and (0,6).

Learn the idea

A line can be represented through slope and point, standard coefficients, or intercepts. Piecewise functions combine different rules on different domains, so choosing the correct branch is part of evaluation. An x-axis point has y=0, and a y-axis point has x=0. Substituting these conditions into a line equation recovers the two coordinate intercepts.

Here is the method on the supplied teaching case. Set y=0 for the x-intercept: x=12/2=6. Set x=0 for the y-intercept: y=12/3=4.

An intercept is an ordered pair, not just a coefficient. Do not swap the axes: the x-intercept sets y to zero, while the y-intercept sets x to zero.

1. Write or sketch the supplied teaching case, labeling its quantities and restrictions.
2. Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
3. Solve the independent check with its changed inputs before revealing feedback.
4. Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.

Check your reasoning

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Take it further

Changed-input task: Find both intercepts of 2x+3y=54. Candidate answers: (A) (18,0) and (0,27) (B) (2,0) and (0,3) (C) (27,0) and (0,18) (D) (54,0) and (0,54). Show the mathematical reason, not only the selected answer. Expected result: (27,0) and (0,18). Set y=0 for the x-intercept: x=54/2=27. Set x=0 for the y-intercept: y=54/3=18.

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