Question

Enter an equation relating the variables in the table. Express any value(s) In your answer as simplified fractions, if necessary. Time (x) 35 42 63 Distance (y) 10 12 18 The equation is y =

Answer 1

To find the equation we have to calculate the slope and the intercept with the y axis, and for the slope we choose 2 piont of the table, I picked (14,4) and (35,10) so the slope is:

`m=(y_2-y_1)/(x_2-x_1)`

and we replace the coordinates

`m=(10-4)/(35-14)=(6)/(21)`

Now with the slope and one of the points (14,4) we can calculate the intersept with the y axis, rplacing x=0

`\begin{gathered} y-y_1=m(x-x_1) \\ y-y_1=m(0-x_1) \end{gathered}`

and we replace the slope and the coordinate

`\begin{gathered} y-4=-(6)/(21)\cdot14 \\ y=4+4 \\ y=8 \end{gathered}`

So the final equation will be:

`y=(6)/(21)x+8`