Algebra

The slope of a line is calculated using the formula (y2 - y1) / (x2 - x1), which in this case is (14 - 2) / (3 - (-1)) = 12 / 4 = 3. A common error resulting in a slope of 4 might occur if the denominator is incorrectly calculated as 3 minus 1 instead of 3 minus negative 1.

The equation |x−3|=7 means the distance from x to 3 is 7, so x−3=7 or x−3=−7, giving x=10 and x=−4. Choice A lists only x=10, overlooking the second possibility; absolute‑value equations always produce two symmetric solutions unless the right side is zero.

This step-by-step process maintains the equation's balance and accuracy, ensuring the correct solution for x. A diagram for this topic isn't available yet — the worked example below walks the same reasoning step by step.

• !Many students incorrectly solve the equation by not maintaining the balance of operations on both sides, leading to an incorrect solution.
• !Some students may try to solve the system of equations by adding or subtracting the equations, but this approach may not work if the coefficients of the variables are not the same. Using substitution ensures that we can solve for one variable in terms of the other and then substitute it into the other equation.
• !Choosing a value like 7 is incorrect because it yields 4(7) - 7 = 21, which does not satisfy the equation.
• !A common error resulting in a slope of 4 might occur if the denominator is incorrectly calculated as 3 minus 1 instead of 3 minus negative 1.
• !Option A is incorrect because if a = 3, then b = 2, which results in a sum of 13 instead of 18.

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