Option C: [tex]\frac{4}{5}[/tex] is the slope of the line
Explanation:
The line passes through the points [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]
We need to find the slope of the line.
The slope can be determined using the formula,
[tex]m=\frac{y_2-y_1}{x_2-x_1}[/tex]
Where the coordinates [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] are [tex](3,-1)[/tex] and [tex](-2,-5)[/tex]
Let us substitute the points in the formula
Thus, we have,
[tex]m=\frac{-5-(-1)}{-2-3}[/tex]
Simplifying, we get,
[tex]m=\frac{-5+1}{-2-3}[/tex]
Adding the numerator and denominator, we have,
[tex]m=\frac{-4}{-5}[/tex]
Cancelling the negative terms, we get,
[tex]m=\frac{4}{5}[/tex]
Thus, the slope of the line is [tex]m=\frac{4}{5}[/tex]
Therefore, Option C is the correct answer.
