Question

• Write the equation of the line represented by each table. I 0 17 3 6 6 5 9 9

Answer 1

For the first table

Let's pick 2 points

x₁ = 0 y₁= 17

x₂ = 3 y₂ = 11

To form the equation, we will use the formula;

`y-y_1=\text{ }(y_2-y_1)/(x_2-x_1)=(x-x_1)`

substitute the values into the formula;

`y-17=(11-17)/(3-0)(x-0)`

Evaluate

`y-\text{ 17 =}(-6)/(3)(x-0)`

y - 17 = -2x

add 17 to both-side of the equation

y= -2x + 17

The above is the equation of the line for the first table

Fo the second table

Let's also pick 2 points

x₁ = 3 y₁= -2

x₂ = 6 y₂ = -4

Substitute into the formula;

`y\text{ - (-2) =}(-4+2)/(6-3)(x-3)`

Evaluate

`y\text{ + 2 =}(-2)/(3)(x\text{ - 3)}`
`y\text{ + 2=-}(2)/(3)x\text{ + 2}`

subtract 2 from both-side of the equation

`y=-(2)/(3)x`

The above is the equation for table 2