Answer:
(1,1) and (7,5) => Slope: 2/3
(1,1) and (5,7) => Slope: 3/2
(2,5) and (-1,2) => Slope:1
(2,5) and (-7,-4) => Slope:1
Step-by-step explanation:
The slope of a line is denoted by m and is given as:
[tex]m = \frac{y_2-y_1}{x_2-x_1}[/tex]
Calculating the slope one by one for each pair.
(1,1) and (7,5):
Let m1 be the slope of this line
Here
(x1,y1) = (1,1)
(x2,y2) = (7,5)
Putting values in formula
[tex]m_1 = \frac{5-1}{7-1}\\= \frac{4}{6}\\=\frac{2}{3}[/tex]
(1,1) and (5,7):
Let m2 be the slope of this line
Here
(x1,y1) = (1,1)
(x2,y2) = (5,7)
Putting values in formula
[tex]m_2 = \frac{7-1}{5-1}\\m_2=\frac{6}{4} = \frac{3}{2}[/tex]
(2,5) and (-1,2):
Let m3 be the slope of this line
Here
(x1,y1) = (2,5)
(x2,y2) = (-1,2)
Putting values in formula
[tex]m_3 = \frac{2-5}{-1-2}\\m_3 = \frac{-3}{-3} = 1[/tex]
(2,5) and (-7,-4):
Let m4 be the slope of this line
Here
(x1,y1) = (2,5)
(x2,y2) = (-7,-4)
Putting values in formula
[tex]m_4 = \frac{-4-5}{-7-2}\\m_4 = \frac{-9}{-9} = 1[/tex]
Hence,
The points and their respective slopes are as follows:
(1,1) and (7,5) => Slope: 2/3
(1,1) and (5,7) => Slope: 3/2
(2,5) and (-1,2) => Slope:1
(2,5) and (-7,-4) => Slope:1
