Question

Colin and Tommy live in different cities. They are both flying from home to London, England.Colin's distance from London over time is shown on the graph.Tommy lives farther from London than Colin, but his plane is flying faster.Which equation could represent Tommy's distance from London in miles, y, after x hours?A y = - 450x + 4000B y = - 550x + 4000C y = - 450x + 5000D y = - 550x + 5000

Answer 1

From the graph, we have the following data,

Remember that the general form for the equation of a straight line is :

`\begin{gathered} y\text{ = mx + c} \\ \text{where m is the slope } \\ c\text{ is the intercept on the ordinate} \end{gathered}`
`\begin{gathered} c\text{ = 4500} \\ m\text{ = }(y_2-y_1)/(x_2-x_1) \\ =\text{ }\frac{0\text{ - 4500}}{9\text{ - 0}} \\ =\text{ -500} \end{gathered}`

Hence, the equation is : y = - 500x + 4500

Since Tommy lives farther than Colin, the equation that could represent his distance from London is : y = -550x + 5000, which corresponds to option D