Question

A scatter plot with a trend line is shown below. Which equation best represents the given data?

Answer 1

B.
`y=(1)/(2)x+5`

Explanation:

We have been given an image of a scatter plot with a trend line. We are asked to find the equation that best represents the given data.

The equation of the line of best fit will best represent the given data. We will write the equation of given line in slope-intercept form of equation:
`y=mx+b`, where, m represents slope of line and b represents the y-intercept.

We will find the slope of given line using points (2,6) and (8,9) as shown below:

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

`m=(9-6)/(8-2)`

`m=(3)/(6)`

`m=(1)/(2)`

Now, we will substitute
`m=(1)/(2)` and coordinates of point (2,6) to find the y-intercept of our given equation.

`6=(1)/(2)* 2+b`

`6=1+b`

`6-1=1-1+b`

`5=b`

Therefore, the equation of line that best represents the given data is
`y=(1)/(2)x+5` and option B is the correct choice.