12 is the fixed travel fee, and 7.50 is the cost for each bag. With $b$ bags, the variable part is $7.50b$, so total cost is $12 + 7.50b$. Option B multiplies the fixed fee by $b$. Option C subtracts the fixed fee inside the bag count. Option D multiplies the fixed fee by the sum, overcounting.

Analyze: speed is constant with 84 miles in 2 hours. Plan: find miles per hour, then multiply by 3.5. Solve: 84 ÷ 2 = 42 mph, then 42 × 3.5 = 147 miles. Check: 3 hours at 42 mph is 126 and half an hour adds 21, totaling 147, which is reasonable. Computing the unit rate first is essential.

B uses the slope formula with arbitrary points $(x_1,3x_1+1)$ and $(x_2,3x_2+1)$, then factors and cancels $(x_2-x_1)$ to conclude $m=3$, correctly naming the slope formula, factoring, and multiplicative inverses. A verifies only one example and does not justify the claim for all points. C misidentifies the slope: in $y=mx+b$, the slope is the coefficient of $x$ (here $3$), not the constant term $1$. D performs an invalid step for determining slope; dividing by $x$ produces $\frac{y}{x}$, which is not the definition of slope between two points and varies with $x$.

A graphing calculator quickly graphs both lines and computes their intersection to decimal accuracy. Solving by hand with these decimals is slower and prone to arithmetic errors. A spreadsheet is not ideal for solving two equations graphically, and mental estimation cannot deliver coordinates to the nearest hundredth.

Analyze: total cost equals fixed fee plus monthly fee. Plan: isolate the $m$ term in $29 + 19m = 181$. Solve: subtract 29 to get $19m = 152$, then divide by 19 to get $m = 8$. Check: $29 + 19(8) = 29 + 152 = 181$. Subtracting 29 first is necessary to isolate $m$.

3 cups corresponds to 12 pancakes. 18 is 1.5 times 12, so the cups also scale by 1.5: $3 \times 1.5 = 4.5$ cups. 3 ignores scaling, 6 doubles instead of multiplying by 1.5, and 1.5 reverses the ratio.

Mental estimation is fastest and sufficient: compare unit prices by rounding and cross-multiplying. For example, $4.59\times 28\approx 4.6\times 28=128.8$ and $5.19\times 24\approx 5.2\times 24=124.8$, so the 28 oz option is slightly cheaper per ounce. A calculator or spreadsheet is slower for an aisle decision, and paper-and-pencil is unnecessary.

D correctly uses the distributive property to get $4x-12$ and then combines like terms $4x$ and $2x$ to obtain $6x-12$. A's factorization changes the expression incorrectly and yields $6x-6$, which is not equivalent. B incorrectly treats $x-3$ as $1x$ and ignores the constant term $-12$. C misapplies distribution (omits multiplying $-3$ by $4$) and then makes an unjustified adjustment to the constant.

Paper-and-pencil algebra lets you clear fractions and isolate $x$ to get an exact value without rounding. Mental estimation will not be precise. A graphing calculator could approximate by graphing two lines but adds setup and may not give an exact fractional answer. A spreadsheet does not handle symbolic manipulation cleanly here.

A correctly expands the left side to $6y-15$, then notes $6y-15=6y-15$ and simplifies to $0=0$, an identity, so the equation is true for all real $y$. B divides by $y$, which is invalid when $y=0$ and unnecessary; it does not justify truth for all $y$. C provides only a single example, which is insufficient to prove the statement for all $y$. D makes an unsupported claim about parity and does not use valid algebraic reasoning.