Graph the line passing through the given point and having the indicated slope. Plot two points on the line. through ( - 1/2 , 4), m = 0

Verified step by step guidance

1. Identify the given point and slope. The point is \(\left(-\frac{1}{2}, 4\right)\) and the slope \(m = 0\).
2. Recall that a slope of zero means the line is horizontal. Therefore, the equation of the line will be of the form \(y = b\), where \(b\) is a constant.
3. Since the line passes through the point \(\left(-\frac{1}{2}, 4\right)\), substitute the \(y\)-coordinate of this point into the equation to find \(b\). This gives \(y = 4\).
4. To plot two points on the line, choose any two different \(x\)-values and use the equation \(y = 4\) to find their corresponding \(y\)-coordinates. For example, if \(x = 0\), then \(y = 4\), and if \(x = 1\), then \(y = 4\).
5. Plot the points \(\left(0, 4\right)\) and \(\left(1, 4\right)\) on the coordinate plane and draw a horizontal line through these points and the original point \(\left(-\frac{1}{2}, 4\right)\).

Key Concepts

Slope of a Line

The slope (m) measures the steepness of a line, defined as the ratio of the vertical change to the horizontal change between two points. A slope of 0 means the line is horizontal, indicating no vertical change as you move along the line.

Equation of a Line Using Point-Slope Form

The point-slope form, y - y₁ = m(x - x₁), allows you to write the equation of a line when given a point (x₁, y₁) and slope m. It helps in finding the line’s equation before graphing or plotting points.

Plotting Points on a Coordinate Plane

Plotting points involves marking coordinates (x, y) on the Cartesian plane. To graph a line, you plot the given point and use the slope to find another point, then draw the line through these points.