1. The problem gives a linear equation for the total cost $y$ of a taxi ride based on miles $x$: $$y = 2.6x + 2.5$$ and a table of values for miles and total cost. 2. We want to verify if the table values satisfy the equation. The formula used is the linear function where $2.6$ is the rate per mile and $2.5$ is the base fee. 3. Check each table entry by substituting $x$ into the equation: - For $x=2$: $$y = 2.6(2) + 2.5 = 5.2 + 2.5 = 7.7$$ The table says $7.50$, which is close but not exact. - For $x=4$: $$y = 2.6(4) + 2.5 = 10.4 + 2.5 = 12.9$$ The table says $13.50$, which is different. - For $x=6$: $$y = 2.6(6) + 2.5 = 15.6 + 2.5 = 18.1$$ The table says $19.50$, which is different. - For $x=8$: $$y = 2.6(8) + 2.5 = 20.8 + 2.5 = 23.3$$ The table says $25.50$, which is different. 4. Since the table values do not match the equation exactly, the statement "The equation $y=2.6x+2.5$ correctly models the total cost in the table" is false. 5. To form a true statement, we can say: "The total cost increases by $6.00$ for every 2 miles, which corresponds to a rate of $3.00$ per mile, and the base fee is $4.50$" because the differences in the table are consistent: - From $7.50$ to $13.50$ is $6.00$ for 2 miles - From $13.50$ to $19.50$ is $6.00$ for 2 miles - From $19.50$ to $25.50$ is $6.00$ for 2 miles 6. So the actual linear model from the table is: $$y = 3x + 1.5$$ (checking for $x=2$: $3(2)+1.5=6+1.5=7.5$ matches the table) 7. Conclusion: The given equation $y=2.6x+2.5$ does not match the table data. The table suggests a different rate and base fee.