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Grade 9 · unit review

Review: Algebra1: Linear Forms and Piecewise Rules

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.

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Bring the unit skills together

Use these 4 new cases to check your reasoning. Choices are temporary and are not saved to an account, sent to staff or recorded as school grades. Download your current review choices before leaving or reloading.

Unit review questions
1. Which line of slope 3 passes through (7,8)?
Need a hint?
  • Point-slope form compares every point’s output displacement with its input displacement from one known point.
  • Subtract the known coordinates in their proper positions: y minus the known y, x minus the known x.
2. What is the slope of 2x+7y=8?
Need a hint?
  • A line in standard form can be solved for y.
  • The y coefficient must divide both the x term and constant.
3. Find both intercepts of 2x+3y=42.
Need a hint?
  • An x-axis point has y=0, and a y-axis point has x=0.
  • An intercept is an ordered pair, not just a coefficient.
4. For f(x)=x when 0≤x≤7, and f(x)=7+2(x−7) when x>7, find f(10).
Need a hint?
  • A piecewise definition names both formulas and the conditions under which each applies.
  • Boundary symbols decide which branch applies at a breakpoint.

The download contains your current choices and any checked feedback. Keep the separate transfer-task work in your own document; downloading its instructions does not mark it complete.

Use the skills in a new task

Create a four-part mathematical solution sheet for these supplied cases. 1. Which line of slope 3 passes through (9,10)? Candidate answers: (A) y+10=3(x+9) (B) y=37x (C) y−10=3(x−9) (D) y−9=3(x−10). 2. What is the slope of 2x+9y=10? Candidate answers: (A) -2/9 (B) -9/2 (C) 10/9 (D) 2/9. 3. 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). 4. For f(x)=x when 0≤x≤9, and f(x)=9+2(x−9) when x>9, find f(12). Candidate answers: (A) 14 (B) 15 (C) 16 (D) 30.

Work on paper or in your own document. Explain the choices you made.

  • State each requested quantity or relationship and its input restrictions.
  • Show intermediate calculations or the applicable theorem with matching correspondences.
  • Give all four results, including exact values or requested rounding and units.
  • Check a result by substitution, reversal, dimensions, a representation or a counterexample as appropriate.
Compare with a model response

1. y−10=3(x−9). Point-slope form is y−y₁=m(x−x₁). Insert m=3, x₁=9, y₁=10. At x=9, the equation gives y=10. 2. -2/9. Solve for y: y=(−2/9)x+10/9. The coefficient of x is the slope, −2/9. 3. (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. 4. 15. 12>9, so choose the second branch, not the first. Substitute: 9+2(12−9)=15. At the boundary the stated first branch applies.

A different response can also meet the criteria. Compare the evidence and reasoning, rather than copying the wording.