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Which equation represents a line that passes through [tex]$(-9,-3)$[/tex] and has a slope of [tex]-6[/tex]?

A. [tex]y - 9 = -6(x - 3)[/tex]
B. [tex]y + 9 = -6(x + 3)[/tex]
C. [tex]y - 3 = -6(x - 9)[/tex]
D. [tex]y + 3 = -6(x + 9)[/tex]

Sagot :

GinnyAnsweridn
To determine which equation represents the line that passes through the point [tex]\((-9, -3)\)[/tex] and has a slope of [tex]\(-6\)[/tex], we can 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.

Given:
[tex]\( (x_1, y_1) = (-9, -3) \)[/tex]
[tex]\( m = -6 \)[/tex]

Plugging these values into the point-slope form, we get:

[tex]\[ y - (-3) = -6(x - (-9)) \][/tex]

This simplifies to:
[tex]\[ y + 3 = -6(x + 9) \][/tex]

So, the equation that represents the line passing through the point [tex]\((-9, -3)\)[/tex] with a slope of [tex]\(-6\)[/tex] is:

[tex]\[ y + 3 = -6(x + 9) \][/tex]

Among the given options, this corresponds to:

[tex]\[ y + 3 = -6(x + 9) \][/tex]

Thus, the correct equation is:

[tex]\[ y + 3 = -6(x + 9) \][/tex]

In the given multiple-choice format, the correct answer is the fourth option:

[tex]\[ y+3=-6(x+9) \][/tex]
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