Question

Could you help me solve this table.For each table find the relation between x and y and then comple the table.

Answer 1

Analyzing the table given in the exercise, you can identify that each input value (x-value) has one and only one output value (y-value). Therefore, the relation is a function.

Notice that "x" is the Independent Variable and "y" is the Dependent Variable.

• Observe that when:

`x=0`

The value of "y" is:

`y=9`

Therefore, the Start value is:

`y=9`

• To find the Rate of change you can follow these steps:

- You can identify these ordered pairs:

`(0,9),(2,8),(4,7),(6,6)`

If you plot them on a Coordinate Plane, you get:

You can identify that it is a line. Therefore, the Rate to change can be found with this formula:

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

In this case, you can choose these points:

`(0,9);(6,6)`

And set up that:

`\begin{gathered} y_2=9 \\ y_1=6 \\ x_2=0 \\ x_1=6 \end{gathered}`

Then, substituting and evaluating, you get:

`m=(9-6)/(0-6)=(3)/(-6)=-(1)/(2)`

• To find the equation for the relation, you need to remember that the

equation of a line can be written in Slope-Intercept Form:

`y=mx+b`

Where "m" is the slope (the rate of change) and "b" is the y-intercept (the start value).

Since you already know both values, you can set up that the equation is:

`y=-(1)/(2)x+9`

• To find the value of "y" when:

`x=100`

You need to substitute that value into the equation and then evaluate:

`\begin{gathered} y=(-(1)/(2))(100)+9 \\ \\ y=-50+9 \\ y=-41 \end{gathered}`

Hence, the answers are:

• Start value:

`y=9`

• Rate of change:

`m=-(1)/(2)`

• Relation:

`y=-(1)/(2)x+9`

• Table: