Response
After her seventh assessment, she will score above 85.
Explanation
We can represent this situation through a linear equation.
On her initial assessment, Rita scored 58, providing the first point (1, 58).
On her second assessment, Rita earned 63, making our second point (2, 63).
To calculate the rate, known as the slope of our line, we utilize the slope formula:
where
signifies the coordinates for the first point
and represents the coordinates for the second point.
From these points, we can establish that ,
,
,
. We will input the values into our slope equation:
Now, we recognize that Rita's score grows by 5 points with every assessment.
To finalize the equation of our line, we apply the point-slope formula:
Ultimately, we substitute with 85 in our equation and solve for
to determine on which assessment she will achieve a score higher than 85:
Since a score of 0.4 assessments is not possible, she will exceed 85 after her seventh assessment.