Option C:
is the slope of the line
Step-by-step explanation:
The line passes through the points
and
![(-2,-5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/cc8iqhco3ntrs4yxeca8mozne54fa2oizy.png)
We need to find the slope of the line.
The slope can be determined using the formula,
![m=(y_2-y_1)/(x_2-x_1)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/e9lgdayfzr27dyurvzbw9lffpiv7535tiv.png)
Where the coordinates
and
are
and
![(-2,-5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/cc8iqhco3ntrs4yxeca8mozne54fa2oizy.png)
Let us substitute the points in the formula
Thus, we have,
![m=(-5-(-1))/(-2-3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/8rejxdsrahy4r8jx67a7wthbds8nk4gwk5.png)
Simplifying, we get,
![m=(-5+1)/(-2-3)](https://img.qammunity.org/2021/formulas/mathematics/high-school/p9gvpkl4jbj0i7n4umtii56c5awkxhcgqi.png)
Adding the numerator and denominator, we have,
![m=(-4)/(-5)](https://img.qammunity.org/2021/formulas/mathematics/high-school/ctfnzwbssy6pikyqvu279icf9ekf9kc0sm.png)
Cancelling the negative terms, we get,
![m=(4)/(5)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/e0g9gpxdvs2zjvgtl0whhvpvlblv7m957f.png)
Thus, the slope of the line is
![m=(4)/(5)](https://img.qammunity.org/2021/formulas/mathematics/middle-school/e0g9gpxdvs2zjvgtl0whhvpvlblv7m957f.png)
Therefore, Option C is the correct answer.