Sure! To find the point-slope equation of a line that contains the point [tex]\((-8, -4)\)[/tex] with a slope of [tex]\(-3\)[/tex], we can use the point-slope form of a linear equation. The point-slope form is given by:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]
where [tex]\((x_1, y_1)\)[/tex] is a point on the line and [tex]\(m\)[/tex] is the slope of the line.
Given:
- The point [tex]\((x_1, y_1) = (-8, -4)\)[/tex]
- The slope [tex]\(m = -3\)[/tex]
Let's substitute these values into the point-slope form equation:
[tex]\[ y - (-4) = -3(x - (-8)) \][/tex]
Simplifying the equation:
[tex]\[ y + 4 = -3(x + 8) \][/tex]
Thus, the point-slope form of the line is:
[tex]\[ y + 4 = -3(x + 8) \][/tex]
So, the correct answer is:
C. [tex]\( y + 4 = -3(x + 8) \)[/tex]
