For this case we have that by definition the constant of variation of a line is given by the slope m, of said line.
Where:
[tex]m = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
To find the slope of a line it is necessary to find two points through which the line passes.
To solve the given problem, we find the slopes of the lines shown in the graphics R and S:
Graphic R:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (2,1)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {R} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {R} = \frac {1-0} {2-0}[/tex]
[tex]m_ {R} = \frac {1} {2}[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {R} = \frac {1} {2}[/tex]
Graphic S:
It is observed that the line passes through the following points:
[tex](x_ {1}, y_ {1}) = (0,0)\\(x_ {2}, y_ {2}) = (1,2)[/tex]
Substituting in the formula of the slope we have:
[tex]m_ {S} = \frac {(y_ {2} -y_ {1})} {(x_ {2} -x_ {1})}[/tex]
[tex]m_ {S} = \frac {2-0} {1-0}[/tex]
[tex]m_ {S} = \frac {2} {1}[/tex]
[tex]m_ {S} = 2[/tex]
Thus, the slope of the line of the graph R is given by: [tex]m_ {S} = 2[/tex]
[tex]m_ {S}> m_ {R}[/tex]
then, the graph S has a variation constant greater than the graph R.
Answer:
The graph S has a variation constant greater than the graph R.
Rachel's idea is wrong
