Answer :
By using the formula of slope of a line, it can be calculated that
Slope of (e) < slope of (g) < slope of (d) < slope of (c) < slope of (b) < slope of (f) < slope of (a)
What is slope of a line?
Slope of a line is the tangent of the angle that the line makes with the positive direction of x axis.
If [tex]\theta[/tex] is the angle that the line makes with the positive direction of x axis, then slope (m) is given by
m = [tex]tan\theta[/tex]
a) The coordinates are (15, 30) and (20, 40)
Slope = [tex]\frac{40 - 30}{20 - 15}\\[/tex]
[tex]= \frac{10}{5}[/tex]
= 2
b) The coordinates are (12, 32) and (18, 48)
Slope = [tex]\frac{48 - 32}{18 - 12}\\[/tex]
[tex]= \frac{16}{6}[/tex]
= [tex]\frac{8}{3}[/tex]
c) The coordinates are (27, 12) and (72, 32)
Slope = [tex]\frac{32 - 12}{72 - 27}\\[/tex]
[tex]= \frac{20}{45}[/tex]
= [tex]\frac{4}{9}[/tex]
d) The coordinates are (45, 15) and (60, 20)
Slope = [tex]\frac{20 - 15}{60 - 45}\\[/tex]
[tex]= \frac{5}{15}[/tex]
= [tex]\frac{1}{3}[/tex]
e) The coordinates are (27, 2) and (243, 18)
Slope = [tex]\frac{18 - 2}{243 - 27}\\[/tex]
[tex]= \frac{16}{216}[/tex]
= [tex]\frac{2}{27}[/tex]
f) The coordinates are (18, 63) and (24, 84)
Slope = [tex]\frac{84 - 63}{24 - 18}\\[/tex]
[tex]= \frac{21}{6}[/tex]
= [tex]\frac{7}{2}[/tex]
g) The coordinates are (63, 9) and (84, 12)
Slope = [tex]\frac{12- 9}{84 - 63}\\[/tex]
[tex]= \frac{3}{21}[/tex]
= [tex]\frac{1}{7}[/tex]
Now, the fractions in increasing order are
[tex]\frac{2}{27} < \frac{1}{7} < \frac{1}{3} < \frac{4}{9} < \frac{8}{3} < \frac{7}{2} < 2[/tex]
So
Slope of (e) < slope of (g) < slope of (d) < slope of (c) < slope of (b) < slope of (f) < slope of (a)
To learn more about slope, of a line refer to the link-
https://brainly.com/question/3493733
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