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Choose the equation below that represents the line passing through the point [tex]\((-2, -3)\)[/tex] with a slope of -6.

A. [tex]\(y + 3 = -6(x + 2)\)[/tex]

B. [tex]\(y + 2 = 6(x + 3)\)[/tex]

C. [tex]\(y - 3 = -6(x - 2)\)[/tex]

D. [tex]\(y - 2 = 6(x - 3)\)[/tex]

Sagot :

GinnyAnswer
To determine which equation represents the line passing through the point [tex]\((-2, -3)\)[/tex] with a slope of [tex]\(-6\)[/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. Let's apply the given point [tex]\((-2, -3)\)[/tex] and the slope [tex]\(-6\)[/tex].

1. Substitute the given point and slope into the point-slope form:

[tex]\[ y - (-3) = -6(x - (-2)) \][/tex]

2. Simplify the equation:

[tex]\[ y + 3 = -6(x + 2) \][/tex]

Hence, the equation that represents the line passing through the point [tex]\((-2, -3)\)[/tex] with a slope of [tex]\(-6\)[/tex] is:

[tex]\[ y + 3 = -6(x + 2) \][/tex]

We can now match this equation with the given options:

1. [tex]\(y+3=-6(x+2)\)[/tex]
2. [tex]\(y+2=6(x+3)\)[/tex]
3. [tex]\(y-3=-6(x-2)\)[/tex]
4. [tex]\(y-2=6(x-3)\)[/tex]

The correct equation is option 1:

[tex]\[ y+3=-6(x+2) \][/tex]

Therefore, the answer is the first option.
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