Question

In the given figure, if the slope of line l is \[m\], then \[m\] is terms of \[h\] is

A.\[\dfrac{h}{{1 + h}}\]
B.\[\dfrac{{ - h}}{{1 + h}}\]
C.\[\dfrac{h}{{1 - h}}\]
D.\[1 + h\]

Answer 1

Hint: Here we have to express the slope of the line \[m\] in terms of \[h\]. We will find the slope of the line using the two points. Then we will equate the value of slope obtained with the given value of slope. We will simplify the equation to get the required.

Complete step-by-step answer:
The given points of the line are \[\left( {0,h + m} \right)\] and \[\left( {h,0} \right)\].
We will find the slope of the line using these two given points.
Therefore,
Slope of line \[ = \dfrac{{0 - \left( {h + m} \right)}}{{h - 0}}\]
Simplifying the given fraction further, we get
Slope of line \[ = \dfrac{{ - \left( {h + m} \right)}}{h}\]
We know the slope of the line is \[m\]. So, substituting the value of slope in above equation, we get
$\Rightarrow$ \[m = \dfrac{{ - \left( {h + m} \right)}}{h}\]
Cross multiplying the terms, we get
$\Rightarrow$ \[mh = - h - m\]
Adding \[m\] on both sides, we get
$\Rightarrow$ \[mh + m = - h - m + m\\\Rightarrow mh + m = - h\]
Rewriting the above equation, we get
$\Rightarrow$ \[m\left( {h + 1} \right) = - h\]
Dividing \[\left( {h + 1} \right)\]on both sides, we get
\[\Rightarrow\dfrac{{m\left( {h + 1} \right)}}{{\left( {h + 1} \right)}} = \dfrac{{ - h}}{{\left( {h + 1} \right)}}\\ \Rightarrow m = \dfrac{{ - h}}{{\left( {h + 1} \right)}}\]
This is the required value of \[m\] in terms of \[h\].
Thus, the correct option is B.

Note: Here we have calculated the value of slope of the given line. A slope is also known as a gradient and it is the ratio of the difference of \[y\] coordinates to the difference of the \[x\] coordinates.
Some important properties of slope are:-
If the value of slope is greater than zero then the line goes up from left to right.
If the value of slope of the line is less than zero then the line goes down from right to left.
The value of slope for horizontal lines is zero.
The value of slope is not defined for vertical lines.