The slope of a line through the pair of coordinates is define as the rate of change in y coordinates with respect to x coordinate
So,
[tex]\text{Slope =}\frac{y_2-y_1}{x_2-x_1}[/tex]1) (2, 10) & (1,5)
[tex]\begin{gathered} \text{Slope =}\frac{y_2-y_1}{x_2-x_1} \\ \text{From the given coordinates we have :} \\ x_1=2,x_2=1,y_1=10,y_2=5 \\ \text{Subctitute the value} \\ \text{SLope =}\frac{5-10}{1-2} \\ \text{Slope}=\frac{-5}{-1} \\ \text{Slope =5} \end{gathered}[/tex]
2). (0,2) (-3,2)
[tex]\begin{gathered} \text{Slope =}\frac{y_2-y_1}{x_2-x_1} \\ \text{From the given coordinates we have :} \\ x_1=0,x_2=-3,y_1=2,y_2=2 \\ \text{Subctitute the value} \\ \text{SLope =}\frac{-3-0}{2-2} \\ \text{Slope}=\frac{-3}{0} \\ \text{Slope =}0 \end{gathered}[/tex]
3). (-4,0) & (0,-3)
[tex]\begin{gathered} \text{Slope =}\frac{y_2-y_1}{x_2-x_1} \\ \text{From the given coordinates we have :} \\ x_1=-4,x_2=0,y_1=0,y_2=-3 \\ \text{Subctitute the value} \\ \text{SLope =}\frac{-3-0}{0-(-4)} \\ \text{Slope}=\frac{-3}{4} \\ \text{Slope =}-\frac{3}{4} \end{gathered}[/tex]
4). (1,3) & (-2,6)
[tex]\begin{gathered} \text{Slope =}\frac{y_2-y_1}{x_2-x_1} \\ \text{From the given coordinates we have :} \\ x_1=1,x_2=-2,y_1=3,y_2=6 \\ \text{Subctitute the value} \\ \text{SLope =}\frac{6-3}{-2-1} \\ \text{Slope}=\frac{3}{-3} \\ \text{Slope =}-1 \end{gathered}[/tex]