Absolutely! Let's find the slope of the line that passes through the points [tex]\((-4, 6)\)[/tex] and [tex]\((-3, -1)\)[/tex].
The formula to calculate the slope [tex]\( m \)[/tex] of a line passing through two points [tex]\((x_1, y_1)\)[/tex] and [tex]\((x_2, y_2)\)[/tex] is:
[tex]\[ m = \frac{y_2 - y_1}{x_2 - x_1} \][/tex]
Given the points [tex]\((-4, 6)\)[/tex] and [tex]\((-3, -1)\)[/tex], let's assign:
- [tex]\( x_1 = -4 \)[/tex]
- [tex]\( y_1 = 6 \)[/tex]
- [tex]\( x_2 = -3 \)[/tex]
- [tex]\( y_2 = -1 \)[/tex]
Substitute these values into the slope formula:
[tex]\[ m = \frac{-1 - 6}{-3 - (-4)} \][/tex]
Now, simplify the numerator and the denominator:
[tex]\[ m = \frac{-1 - 6}{-3 + 4} \][/tex]
[tex]\[ m = \frac{-7}{1} \][/tex]
So, the slope [tex]\( m \)[/tex] of the line through the points [tex]\((-4, 6)\)[/tex] and [tex]\((-3, -1)\)[/tex] is:
[tex]\[ m = -7 \][/tex]
Therefore, the correct answer is:
[tex]\[ -\frac{7}{1} \][/tex]
