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.