To solve the problem, we need to determine the rate at which tests are conducted per week, which is represented by the slope of the line. The slope of a line in this context can be calculated using the formula for slope, which is "rise over run."
Here, the "rise" corresponds to the number of tests (27 tests), and the "run" corresponds to the number of weeks (36 weeks). Therefore, the slope [tex]\( m \)[/tex] is calculated by dividing the number of tests by the number of weeks:
[tex]\[ m = \frac{\text{number of tests}}{\text{number of weeks}} \][/tex]
Substituting the given values:
[tex]\[ m = \frac{27 \text{ tests}}{36 \text{ weeks}} = \frac{27}{36} \][/tex]
To simplify [tex]\(\frac{27}{36}\)[/tex], we divide both the numerator and the denominator by their greatest common divisor (GCD). The GCD of 27 and 36 is 9.
Thus:
[tex]\[ m = \frac{27 \div 9}{36 \div 9} = \frac{3}{4} \][/tex]
Therefore, the slope of the line that represents the number of tests on the [tex]\( y \)[/tex]-axis and the time in weeks on the [tex]\( x \)[/tex]-axis is:
[tex]\[ \boxed{\frac{3}{4}} \][/tex]
The correct answer is A. [tex]\(\frac{3}{4}\)[/tex].
