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

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

`(17-3)/(3-1)=(14)/(2)=7`

Similarly,

`(66-17)/(10-3)=(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.