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Usimov [2.4K]
2 years ago
9

A school conducts 27 tests in 36 weeks. Assume the school conducts tests at a constant rate. What is the slope of the line that

represents the
number of tests on the y-axis and the time in weeks on the x-axis?
A.3/4
B.4/3
C. 3
D.4
Mathematics
2 answers:
Nikitich [7]2 years ago
5 0

The correct result is 3/4

We know that the formula is given by:

\boxed{\large \sf m=\dfrac{y_{2} - y_{1} }{x_{2} -x_{1} }}

  • Being the following data of this question

*27 tests << y

*36 weeks << x

<h3>         </h3>

Then, the resolution will be:

{\large \sf m=\dfrac{y_{2} - y_{1} }{x_{2} -x_{1} }}

{\large \sf m=\dfrac{27-0 }{ 36-0 }}

{\large \sf m=\dfrac{27^{\div 9}  }{ 36^{\div9}  }}

\blue{\boxed{\large \sf m=\dfrac{3 }{ 4  }}}\\

So, the answer is 3/4.

NeTakaya2 years ago
4 0

Answer:

The slope of the line that represents the number of tests on the y-axis and the time in weeks on the x-axis is \frac{3}{4}.

Step-by-step explanation:

<h3>Definition of slope of a line:</h3>

The slope of a line describes its steepness. In mathematical terms, for a line passing through two points with known coordinates, the slope is defined as the ratio of the change in the y-coordinates to the change in the x-coordinates.

<h3>Formula for the slope of a line:</h3>

Let 'm' represent the slope of a line passing through two points with coordinates (x_{1},y_{1}) and (x_{2},y_{2}). So, according to the definition, the slope of the line can be written as follows,

m=\left|\frac{y_{2}-y_{1}  }{x_{2}-x_{1}}\right|

<h3>Calculation of slope:</h3>

According to the information given in the question, the school conducts 27 tests in 36 weeks.

Now, any point on the x- axis is given by the general form (x,0), where  x  represents any numerical value on the axis. Similarly, any point on the y- axis is given by the general form (0,y), where y represents any numerical value on the axis.

It is given that the time in weeks is represented on the x- axis, so 36 weeks can be represented as coordinates as (36,0). Likewise, the number of tests conducted, i.e., 27 can be represented as coordinates as (0,27).

Now, slope of the line passing through the above mentioned points, using the formula is as follows,

m=\left| \frac{27-0}{0-36} \right|\\m=\left| \frac{27}{-36} \right|\\\\m=\left| \frac{3}{-4} \right|\\\\

Simplifying the mod operator, the slope of the line is found to be \frac{3}{4}.

Hence, the correct option is option A.  \frac{3}{4}.

To know more about the slope of the line and its significance, visit https://brainly.ph/question/3226543  

   

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