Answer:
The slope of the line that passes through the pair of points (1, 7) and (10, 1) is \(\frac{-2}{3}\)
The slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1) is -1
The slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2) is \(\frac{-33}{16}\)
Step-by-step explanation:
Formula of slope of line (m) : \(\frac{y_2-y_1}{x_2-x_1}\)
Part 1 : Points are (1, 7) and (10, 1)
\((x_1,y_1) =(1,7)\)
\((x_2,y_2) =(10,1)\)
So, using formula
Slope (m) \(=\frac{1-7}{10-1}\)
\(=\frac{-6}{9}\)
\(=\frac{-2}{3}\)
Thus the slope of the line that passes through the pair of points (1, 7) and (10, 1) is \(\frac{-2}{3}\)
Part 2:Points (-5.5, 6.1) and (-2.5, 3.1)
\((x_1,y_1) =(-5.5,6.1)\)
\((x_2,y_2) =(-2.5,3.1)\)
So, using formula
Slope (m) \(=\frac{3.1-6.1}{-2.5-(-5.5)}\)
\(=\frac{-3}{3}\)
\(= -1\)
Thus the slope of the line that passes through the points (-5.5, 6.1) and (-2.5, 3.1) is -1
Part 3 : Points (-7/3, -3) and (-5, 5/2)
\((x_1,y_1) =(-7/3,-3)\)
\((x_2,y_2) =(-5,5/2)\)
So, using formula
Slope (m) \(=\frac{\frac{5}{2}-(-3)}{-5-(\frac{-7}{3})}\)
\(=\frac{\frac{5}{2}+3}{-5+\frac{7}{3}}\)
\(=\frac{-33}{16}\)
Thus the slope of the line that passes through the pair of points (-7/3, -3) and (-5, 5/2) is \(\frac{-33}{16}\)
