Ratios, Rates, and Linear Relationships: mastery check

Verify the proposed result “Yes, because $11 = 4(3) - 1$.” against the original statement.

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Complete the calculation after “Evaluate $3x + 1$ at $x = 2, -1,$ and $4$.” in this problem: Which of $(2, 7), (-1, -2),$ and $(4, 10)$ satisfy $y = 3x + 1$?

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Name and justify the most efficient first move, then solve: Find the missing coordinate $k$ if (k, $14)$ lies on $2x + y = 22$.

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Compare the methods used in these two cases and identify the structural reason they differ: Which of $(2, 7), (-1, -2),$ and $(4, 10)$ satisfy $y = 3x + 1$? Find the missing coordinate $k$ if (k, $14)$ lies on $2x + y = 22$.

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Create the representation most useful for checking this result: Which of $(2, 7), (-1, -2),$ and $(4, 10)$ satisfy $y = 3x + 1$? Coordinate the context, a table of ordered pairs, the graph, and a linear equation with labeled units.

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A learner reports “Yes, because $11 = 4(3) - 1$.” but omits the original-condition check. Explain the risk before deciding whether the result is supported.

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Repair a solution that skips “Solve $2k + 14 = 22$.” while solving: Find the missing coordinate $k$ if (k, $14)$ lies on $2x + y = 22$.

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In this coordinate plane and equation solutions case, change one numerical value, solve the revised problem, and identify which parts of the original method still apply: Decide whether the point $(3, 11)$ lies on $y = 4x - 1$.

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Connect the opening situation “Test whether points belong to a relationship.” to the algebraic structure used in the worked case. Define quantities and units before writing any equation.

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Explain why the method for coordinate plane and equation solutions is valid here and name one nearby problem where it would not apply.

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Compare the conclusions of all three worked cases with this lesson outcome—Interpret graph points as ordered pairs satisfying an equation. Explain what remains invariant across them.

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Exit check: solve and verify without referring to the displayed steps. Which of $(2, 7), (-1, -2),$ and $(4, 10)$ satisfy $y = 3x + 1$?

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Exit check: solve and verify without referring to the displayed steps. Find the missing coordinate $k$ if (k, $14)$ lies on $2x + y = 22$.

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Classify the mathematical object and requested action in this lesson case: Find and interpret both intercepts of $3x + 2y = 12$.

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State the central definition behind this outcome: Find and interpret where one quantity is zero.

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Before calculating, list every sign, endpoint, unit, grouping, or domain condition that can affect: Find and interpret both intercepts of $3x + 2y = 12$.

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Explain why this opening move is valid: Set $y = 0$ to find the horizontal intercept.

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Find and interpret both intercepts of$$3x + 2y = 12$$

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Find both intercepts of$$4x - 5y = 20$$

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A subscription cost is C $= 12m + 35,$ where $m$ is the number of months. Interpret the vertical intercept and determine whether a horizontal intercept is meaningful.

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Verify the proposed result “x-intercept $(4, 0)$ and y-intercept $(0, 6)$.” against the original statement.

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Complete the calculation after “Set $y = 0$ and solve $4x = 20$.” in this problem: Find both intercepts of $4x - 5y = 20$.

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Name and justify the most efficient first move, then solve: A subscription cost is C $= 12m + 35,$ where $m$ is the number of months. Interpret the vertical intercept and determine whether a horizontal intercept is meaningful.

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Compare the methods used in these two cases and identify the structural reason they differ: Find both intercepts of $4x - 5y = 20$. A subscription cost is C $= 12m + 35,$ where $m$ is the number of months. Interpret the vertical intercept and determine whether a horizontal intercept is meaningful.

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