She will be scoring above 85 after her 7 assessment.
<h2>Explanation</h2>We can model this situation using a line equation.
We know that on her first assessment, Rita scored 58 points, so our first point is (1, 58)
We also know that on her second assessment, Rita scored 63 points, so our second point is (2, 63)
To find the rate, which is the slope of our line, we are using the slope formula:
where
are the coordinates of the first point
are the coordinates of the second point
From our points we can infer that ,
,
,
. Let's replace the values in our slope formula:
Now we know that Rita's score is increasing 5 points every assessment.
To complete the equation of our line, we are using the point slope formula:
Finally, we just need to replace with 85 in our line equation and solve for
to find after which assessment she will score above 85:
Since we can't have 0.4 assessment, she will be scoring above 85 after her 7 assessment.