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

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 :

GinnyAnswer
To find the equation of a line that passes through the point \((-9, -3)\) and has a slope of \(-6\), 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 \((x_1, y_1)\) is a point on the line, and \(m\) is the slope.

Given:
- Point \((x_1, y_1) = (-9, -3)\)
- Slope \(m = -6\)

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

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

Simplify the equation:
[tex]\[ y + 3 = -6(x + 9) \][/tex]

So, the equation of the line in point-slope form that passes through \((-9, -3)\) with a slope of \(-6\) is:

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

Now, let's match this equation with the given options:

1. \( y - 9 = -6(x - 3) \)
2. \( y + 9 = -6(x + 3) \)
3. \( y - 3 = -6(x - 9) \)
4. \( y + 3 = -6(x + 9) \)

The equation \( y + 3 = -6(x + 9) \) matches option 4.

Therefore, the equation that represents a line passing through \((-9, -3)\) and having a slope of \(-6\) is:

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

Thus, the correct option is 4
f4shore

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Hello! In this question, we are trying to figure out which equation represents the line that follows the given parameters.

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Explanation:

We are given the following information:

  • Line passes through the point (-9, -3)
  • Slope of -6

We also need to find our answer using the point-slope equation, as the answer choices follow this format:

y - y1 = m(x - x1)

Where:

  • m = slope
  • (x1, y1) is the coordinate point

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Solve:

Using the given information, we are able to solve the question.

We know that our slope is -6, which is m in our formula, so we could plug -6 into m to get closer to our answer:

y - y1 = -6(x - x1)

Now, since we know our coordinate point is (-9, -3), we can plug in our coordinate into the corresponding variable to complete our equation:

y - (-3) = -6(x - (-9))

Simplify:

y + 3 = -6(x + 9)

Therefore, this equation matches with answer choice D). y + 3 = -6(x + 9)

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Answer:

D). y + 3 = -6(x + 9)

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