Question

I NEED HELP ON THIS

Answer 1

From the given table and options, we can note a linear behavior. Lets find the slope m and the y-intercept b for our table. As we know the line equation is

`y=mx+b`

where the slope m is given by

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

where the values on the right hand side come from 2 points of our table, for instance, we can choose points

`\begin{gathered} (x_1,y_1)=(2,32) \\ (x_2,y_2)=(5,50) \end{gathered}`

by substtuting these values into the slope formula, we get

`m=(50-32)/(5-2)`

which gives

`\begin{gathered} m=(18)/(3) \\ m=6 \end{gathered}`

then, our line equation has the form

`y=6x+b`

In order to find b, we must substitute one of the 2 choosen points, if we substitute point (2,32), we get

`32=6(2)+b`

then, we have

`\begin{gathered} 32=12+b \\ 32-12=b \\ b=20 \end{gathered}`

then, the searched line is

`y=6x+20`

which corresponds to the last option