Question

Misty correctly determined the equation of the linear function represented by the table of values below to be y = negative 2 x + 9 in slope-intercept form by using the ordered pairs (1, 7) and (2, 5).

Answer 1

we can verify that the determined equation is the same as the equation determines by Misty, hence, we conclude that Misty had correctly determined the equation of the linear function.

Explanation:

As Misty determined the equation of linear function:

`y=-2x+9`

We need to check whether she has got the correct equation or not.

As the linear equation passes through the points
`(1, 7)` and
`(2, 5)`.

Finding the slope:

The slope between two points
`(1, 7)` and
`(2, 5)`

`\left(x_1,\:y_1\right)=\left(1,\:7\right),\:\left(x_2,\:y_2\right)=\left(2,\:5\right)`

`m=(5-7)/(2-1)`

`m=-2`

As we know the point-slope form is:

`y-y_1=m\left(x-x_1\right)`

So, the equation of the line will be:

`y-y_1=m\left(x-x_1\right)`

`y-5=-2\left(x-2\right)`

Add 5 to both sides

`y-5+5=-2\left(x-2\right)+5`

`y=-2x+9`

From the above calculation, we can verify that the determined equation is the same as the equation determines by Misty, hence, we conclude that Misty had correctly determined the equation of the linear function.