Question

How do you calculate the slope of $\left( {{\mathbf{0}},{\mathbf{5}}} \right)$ and $\left( {{\mathbf{5}},{\mathbf{0}}} \right)?$

Answer 1

Hint : Slope denotes the steepness and direction of lines. If a line passes through two points $({x_1},{y_1})$ and $({x_2},{y_2})$ , then its slope $m$ is given by the formula $m = \dfrac{{\Delta y}}{{\Delta x}} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}}$ .

Complete step-by-step answer :
In this question we have to find the slope of a line with coordinate points $(0,5)$ and $(5,0)$ .
We know that the formula to find slope of an equation when two points are given is:
$m = \dfrac{{\Delta y}}{{\Delta x}} = \dfrac{{{y_2} - {y_1}}}{{{x_2} - {x_1}}} - - - (1)$
In the given question, let $({x_1},{y_1}) = (0,5)$ and $({x_2},{y_2}) = (5,0)$ .
Here, ${x_1} = 0$ , ${y_1} = 5$ and ${x_2} = 5$ , ${y_2} = 0$ .
Using these values let us now find the value of slope $m$ .
First, let us find the value of $\Delta y$ .
$\Delta y = {y_2} - {y_1} = 0 - 5 \\\ \Rightarrow \Delta y = - 5 \;$
Similarly, let us find the value of $\Delta x$ .
$\Delta x = {x_2} - {x_1} = 5 - 0 \\\ \Rightarrow \Delta x = 5 \;$
Now, let us substitute these values in the equation of slope, equation $(1)$ ,
$m = \dfrac{{ - 5}}{5} \\\ \Rightarrow m = - 1 \;$
Thus, the slope of $(0,5)$ and $(5,0)$ is found to be $- 1$ .
So, the correct answer is “-1”.

Note : The value of slope changes as the number changes. Hence, while substituting the values for ${x_1},{y_1},{x_2},{\text{ and }}{{\text{y}}_2}$, we have to make sure right value Is substituted. Or else the value of slope will be altered. A slope can be positive, negative, constant, and undefined.
$\bullet$ The slope is positive, that is, $m > 0$ , when the line goes up from left to right.
$\bullet$ The slope is negative, that is, $m < 0$ , when the line goes down from left to right.
$\bullet$ The slope is zero or constant, when the line is horizontal.
$\bullet$ The slope is undefined, when the line is vertical.