Recover Slope from Standard Form
A line in standard form can be solved for y.
About 20 minutes, plus any extended practice
Supplied materials
- Paper or a browser scratch area; a calculator is optional unless rounding is requested.
- Supplied teaching case: What is the slope of 2x+2y=3? Candidate answers: (A) -1 (B) 1 (C) 2 (D) 3/2.
- Independent check inputs: What is the slope of 2x+3y=4? Candidate answers: (A) -2/3 (B) -3/2 (C) 2/3 (D) 4/3.
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. A line in standard form can be solved for y. Once written as y=mx+b, the x coefficient gives slope, including the sign introduced while moving the x term.
Here is the method on the supplied teaching case. Solve for y: y=(−2/2)x+3/2. The coefficient of x is the slope, −2/2.
The y coefficient must divide both the x term and constant. Reading the x coefficient directly from unsolved standard form gives the wrong slope unless the y coefficient already equals one.
- Write or sketch the supplied teaching case, labeling its quantities and restrictions.
- Apply the method shown in the worked solution, keeping each intermediate equality or justified inference.
- Solve the independent check with its changed inputs before revealing feedback.
- Complete the three practice cases; explain which mathematical rule rules out one distractor in each case.
See the method in action
Teaching case: What is the slope of 2x+2y=3? Candidate answers: (A) -1 (B) 1 (C) 2 (D) 3/2. Solution: Solve for y: y=(−2/2)x+3/2. The coefficient of x is the slope, −2/2. The final answer is -1. The y coefficient must divide both the x term and constant. Reading the x coefficient directly from unsolved standard form gives the wrong slope unless the y coefficient already equals one.
Check your reasoning
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Helpful tips
- A line in standard form can be solved for y.
- The y coefficient must divide both the x term and constant.
See the answer and explanation
-2/3
Solve for y: y=(−2/3)x+4/3. The coefficient of x is the slope, −2/3.
Take it further
Changed-input task: What is the slope of 2x+9y=10? Candidate answers: (A) -2/9 (B) -9/2 (C) 10/9 (D) 2/9. Show the mathematical reason, not only the selected answer. Expected result: -2/9. Solve for y: y=(−2/9)x+10/9. The coefficient of x is the slope, −2/9.
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More practice: try new cases
Choose an answer for each problem. Explain your method on paper, then use the feedback to decide what to revisit.
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