Given information:

The slope between two points with the coordinates (x1,y1) and (x2,y2) is (y2−y1)/(x2−x1)

Program:

//header file
#include <iostream>
//using the namespace
usingnamespacestd;
intmain()
{
//declaring the variables
floatline_slope, a1 =3, a2 =8, b1 =7, b2 =12;
//calculating the slope of the line connecting two points
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope of the line_slope
cout<<"Slope of a line is: "<<line_slope<<endl;
//return statement
return0;
}

Explanation:

The above code is used to calculate the slope of a line connecting the two points.

Firstly, declaring the variables of float data type. The variable line_slope will store the slope of the line, a1, a2 and b1, b2 is used to store the coordinates point values of x1, x2 and y1, y2.

The slope of a line is calculated by the given formula (y2−y1)/(x2−x1) .

Sample output: -

Given information: formula to calculate the slope: - (y2−y1)/(x2−x1)

Slope of the line is 1

Explanation:

Now, calculating the slope of the line by manual calculating to verify the result of the above program.

  slope=( y 2− y 1)  /( x 2− x 1)=5/5=1

Since, the slope of the line is 1.

Hence, verified

Given information:formula to calculate the slope: - (y2−y1)/(x2−x1)

a1 = 2, a2 = 12 and b1 = 10, b2 = 6

Program:

//header file
#include <iostream>
//using the namespace
usingnamespacestd;
intmain()
{
//declaring the variables
floatline_slope, a1 =2, a2 =12, b1 =10, b2 =6;
//calculating the slope of the line connecting two points
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope of the line_slope
cout<<"Slope of a line is: "<<line_slope<<endl;
//return statement
return0;
}

Sample output: -

Explanation:

The slope of a line is calculated by same formula as used in the exercise 1.a(y2−y1)/(x2−x1)

In the above program only the value of the coordinates point has changed.

Given information:New coordinates point values: - (2, 3) and (2, 4)

Explanation:

While calculating the slope of a line where the coordinates point values are (2, 3) and (2, 4)thanthe values of x1, and x2 are 2 same and the values of y1, and y2 are 3 and 4,here the denominator value is zero as the expression (x2-x1) is equal to zero.

In this case, the value of the slope will be infinite. This situation can be handled by using a conditional statement given below: -

//header file
#include <iostream>
//using the namespace
usingnamespacestd;
intmain()
{
//declaring the variables
floatline_slope, a1 =2, a2 =2, b1 =3, b2 =4;
//calculating the slope of the line connecting two points
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope of the line_slope
cout<<"Slope of a line is: "<<line_slope<<endl;
//to check when the denominator is equal to zero
if((a2 - a1 ==0))
{
	//message
	cout<<"The slope of the line is infinite."<<endl;
}
//return statement
return0;
}

Sample output: -

Given information:The format of the output is xxx.xx

Program:

#include <iostream>
#include <iomanip>
//using the namespace
//for using the standard I/O 
usingnamespacestd;
intmain()
{
//declaring the variables
	//as per the requirement
floatline_slope, a1 =12, a2 =7, b1 =8, b2 =3;
//calculating the slope
	//by usinf the given formula
line_slope=(b2 - b1)/(a2 - a1);
//displaying the slope and settingthe format of output as xx.xxx
//the width is set to 6 and the number of digits after decimal is //set //to 2
cout<<"The value of the slope is "<<setw(6)<<setiosflags(ios::fixed )<<setprecision(2)<<line_slope<<endl;
//return statement
return0;
}

Sample output: -