Question

b.InOut133171066co38Rule:

Answer 1

Suppose that the rule is of the form

$y=mx+b$

Where m is the slope and b is the intercept

The slope can be found using the formula

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

You can take any two consecutive x and y values from the given table.

$\frac{17-3}{3-1}=\frac{14}{2}=7$

Similarly,

$\frac{66-17}{10-3}=\frac{49}{7}=7$

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

$(x,y)=(1,3)$

Now substitute them in the slope-intercept equation.

$\begin{gathered} y=7x+b \\ 3=7(1)+b \\ 3=7+b \\ b=-7+3 \\ b=-4 \end{gathered}$

So the rule is

$y=7x-4$

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.

$\begin{gathered} y=7(1)-4=7-4=3 \\ y=7(3)-4=21-4=17 \\ y=7(10)-4=70-4=66 \\ y=7(6)-4=42-4=38 \end{gathered}$

As you can see, we have got the same results therefore, the rule is correct.