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What is the equation of the line that has a slope of [tex]\(-4\)[/tex] and goes through [tex]\((-1,6)\)[/tex]?

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]

Sagot :

GinnyAnsweridn
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]
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