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Point-slope form is a useful way to write the equation of a line when you know a point on the line and the slope. The general formula is: \[ y - y_1 = m(x - x_1) \]
This equation says that the difference in the y-values between two points on the line is equal to the slope m times the difference in the x-values.
In the given problem, we have the point \((-9, -4)\) and a slope \(m = 0\).
Substituting these into the formula gives: \[ y - (-4) = 0(x - (-9)) \]
which simplifies to: \[ y + 4 = 0 \]
It's important to remember that point-slope form can be transformed into other forms of linear equations by simplifying and solving for \(y\). Understanding how to use the point-slope form can make finding the equation of a line quick and straightforward.

A horizontal line is a special type of line in a coordinate plane that has a constant y-value for all x-values. This means it does not rise or fall as you move left or right along the x-axis.
For a horizontal line, the slope \(m\) is 0. This is because the rise or change in y-values is 0, regardless of the run or change in x-values.
In the example from the exercise, we have a point \((-9, -4)\) and a slope of 0, which clearly indicates a horizontal line. Any point along the line will have the same y-value, which we've determined to be \(-4\).
The equation of a horizontal line therefore takes the form: \[ y = b \]
where \(b\) is the y-value of any point through which the line passes.
In this case, the equation simplifies directly to: \[ y = -4 \]
Understanding horizontal lines helps in recognizing patterns and simplifying equations more efficiently.

A linear equation represents a straight line on a graph and can be written in various forms, with the most common being slope-intercept form and point-slope form.
Slope-intercept form is written as: \[ y = mx + b \]
where \(m\) is the slope and \(b\) is the y-intercept of the line.
Point-slope form, as discussed previously, is written as: \[ y - y_1 = m(x - x_1) \]
Both forms are interchangeable with the right information (points and slope). Linear equations are fundamental because they describe a constant rate of change.
For example, if you know the line goes through the point \((-9, -4)\) with a slope of 0, you can directly find the linear equation as: \[ y = -4 \]
This is a simplified linear equation of a horizontal line where the slope is zero and the y-value is constant. Understanding linear equations is key to numerous areas of math and science, as they model real-world situations with constant rates of change, helping us predict and understand outcomes easily.