Question

What is the equation for this situation? The table shows a representation of the number of miles a car drives over time. Hours, Miles, y Which could NOT be a point on this table? 3 195 4 260 5 325 6 390 Pattern: Eachx value is multiplied by 65 to get each y value.

Answer 1

To find the equation, first, we have to find the ratio of change which is the slope.

$m=\frac{y_2-y_1}{x_2-x_1}$

Replacing the points (3,195) and (5,325), we have

$m=\frac{325-195}{5-3}=\frac{130}{2}=65$

Once we have the slope, we use one point and the point-slope formula to find the equation.

$\begin{gathered} y-y_1=m(x-x_1) \\ y-195=65(x-3) \\ y-195=65x-195 \\ y=65x-195+195 \\ y=65x \end{gathered}$

Therefore, the equation is y = 65x.

All the points on the table must follow the pattern or equation. A point that shouldn't be on the table is (8,455) because if you multiply 8 times 65 you get 520, not 455.

Therefore, a point that couldn't be on this table is (8,455).