Question

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

Answer 1

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:

Definition of slope of a line:

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.

Formula for the slope of a line:

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,

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

Calculation of slope:

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  

   

Answer 2

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

       

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.