What is the equation of a line that passes through the point (-1, -9) and has a slope of zero?

Understand the Problem

The question is asking for the equation of a line that has a slope of zero and passes through the point (-1, -9). A slope of zero indicates a horizontal line, which means the equation will be y = c, where c is a constant equal to the y-coordinate of the given point.

Answer

The equation is $ y = -9 $.

Steps to Solve

Identify the characteristics of the line

Since the slope is zero, we know that the line is horizontal. Horizontal lines can be expressed with the equation ( y = c ), where ( c ) represents a constant.

Determine the constant value

The line must pass through the point (-1, -9). This means that when ( x = -1 ), ( y ) must equal (-9). Hence, the value of ( c ) is (-9).

Write the equation of the line

Now that we established that the line is horizontal and the y-value remains constant at (-9), we can formulate the equation as: $$ y = -9 $$

The equation of the line is ( y = -9 ).

More Information

This equation represents a horizontal line that crosses the y-axis at (-9). Regardless of the x-coordinate, the y-coordinate will always be (-9).

Tips

Confusing a zero slope line with a vertical line: Remember, a zero slope indicates a horizontal line, not vertical.
Forgetting to use the y-coordinate from the given point while forming the equation.

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