To determine the equation of the line that has a slope of -4 and passes through the point [tex]\((-1, 6)\)[/tex], we will use the point-slope form of the equation of a line. 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. In this problem, the slope [tex]\(m\)[/tex] is [tex]\(-4\)[/tex] and the point given is [tex]\((-1, 6)\)[/tex].
Let's substitute the given point and slope into the point-slope formula:
1. Substitute the slope [tex]\(m = -4\)[/tex]:
[tex]\[ y - 6 = -4(x - (-1)) \][/tex]
2. Simplify the expression [tex]\(x - (-1)\)[/tex] to [tex]\(x + 1\)[/tex]:
[tex]\[ y - 6 = -4(x + 1) \][/tex]
This is the equation of the line in point-slope form. Now, let's compare it with the given answer choices:
- A. [tex]\(y + 6 = -4(x + 1)\)[/tex]
- B. [tex]\(y + 6 = -4(x - 1)\)[/tex]
- C. [tex]\(y - 6 = -4(x + 1)\)[/tex]
- D. [tex]\(y - 6 = -4(x - 1)\)[/tex]
Our derived equation [tex]\(y - 6 = -4(x + 1)\)[/tex] matches with option C.
Therefore, the correct answer is:
C. [tex]\(y - 6 = -4(x + 1)\)[/tex]
