Question

Using the digits 0-9, at most one time each, create five ordered pair that represent a linear

function that has a greater rate of change than the following (explain how u got that answer)

Answer 1

(-9, 0), (-8, 1), (-7, 2), (-6, 3) and (-5, 4)

Explanation:

From the graph attached,

Ordered pairs which lie on the given line (-9, 0), (0, 3), (3, 4), (6, 5) and (9, 6).

Since all the points lie on the same line, rate of change of the linear function will be defined by the slope of the given line.

Slope of the line passing through (0, 3) and (3, 4) =
`(y_2-y_1)/(x_2-x_1)`

=
`(4-3)/(3-0)`

`m_1` =
`(1)/(3)`

Now we have to find the ordered pairs which represent a linear function having slope greater than
`(1)/(3)`.

So the points will be (-9, 0), (-8, 1), (-7, 2), (-6, 3) and (-5, 4).

Slope of the linear function passing through (-9, 0) and (-8, 1)

`m_2` =
`(y_2-y_1)/(x_2-x_1)`

=
`(1-0)/(-8+9)`

= 1

Here
`m_2>m_1`