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What is the point-slope form of the equation for the line with a slope of [tex]\(-2\)[/tex] that passes through the point [tex]\((4, -6)\)[/tex]?

A. [tex]\(y - 4 = -2(x + 6)\)[/tex]

B. [tex]\(y + 6 = -2(x - 4)\)[/tex]

C. [tex]\(y - 6 = -2(x + 4)\)[/tex]

D. [tex]\(y = -2x - 6\)[/tex]

Sagot :

GinnyAnsweridn
To find the equation of a line in point-slope form, we use the formula:
[tex]\[ y - y_1 = m(x - x_1) \][/tex]

Here:
- [tex]\( m \)[/tex] is the slope of the line.
- [tex]\((x_1, y_1)\)[/tex] are the coordinates of a point on the line.

Given:
- The slope, [tex]\( m \)[/tex], is [tex]\(-2\)[/tex].
- The point [tex]\((x_1, y_1)\)[/tex] through which the line passes is [tex]\((4, -6)\)[/tex].

Now, substitute the given values into the point-slope form formula:

[tex]\[ y - (-6) = -2(x - 4) \][/tex]

Simplify the equation:

[tex]\[ y + 6 = -2(x - 4) \][/tex]

Thus, the point-slope form of the equation for the line with a slope of [tex]\(-2\)[/tex] that passes through the point [tex]\((4, -6)\)[/tex] is:
[tex]\[ y + 6 = -2(x - 4) \][/tex]

Therefore, the correct option is:
[tex]\[ y + 6 = -2(x - 4) \][/tex]
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