Respuesta :
Suppose that the rule is of the form
[tex]y=mx+b[/tex]Where m is the slope and b is the intercept
The slope can be found using the formula
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]You can take any two consecutive x and y values from the given table.
[tex]\frac{17-3}{3-1}=\frac{14}{2}=7[/tex]Similarly,
[tex]\frac{66-17}{10-3}=\frac{49}{7}=7[/tex]As you can see, you will end up with the same slope.
Now let us find the intercept b.
Take any x, y coordinates from the table
[tex](x,y)=(1,3)[/tex]Now substitute them in the slope-intercept equation.
[tex]\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}[/tex]So the rule is
[tex]y=7x-4[/tex]Verification:
Let us verify whether we got the correct rule or not
Substitute the input x coordinates into the rule and check the outputs y coordinates.
[tex]\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}[/tex]As you can see, we have got the same results therefore, the rule is correct.
