Graph the line passing through the given point and having the indicated slope. Plot twopoints on the line. See Example 7. through ( - 1/2 , 4), m = 0

Verified step by step guidance

1. Step 1: Understand the problem. We are asked to graph a line that passes through the point (-1/2, 4) and has a slope of 0. The slope of a line is the change in y divided by the change in x. Since the slope is 0, this means that for any change in x, the change in y is 0. In other words, y is always the same value, which is the y-coordinate of the given point, 4.
2. Step 2: Plot the given point (-1/2, 4) on the graph. This is the first point on the line.
3. Step 3: Since the slope is 0, we know that the line is horizontal. This means that for any x-coordinate, the y-coordinate will always be 4. So, we can choose any other x-coordinate and the y-coordinate will be 4. For example, we can choose the point (0, 4).
4. Step 4: Plot the second point (0, 4) on the graph. This is the second point on the line.
5. Step 5: Draw a straight line through the two points. This is the graph of the line.

Key Concepts

Slope-Intercept Form

The slope-intercept form of a linear equation is expressed as y = mx + b, where m represents the slope and b is the y-intercept. This form is useful for quickly identifying the slope of a line and where it crosses the y-axis. Understanding this format allows students to easily graph lines by starting at the y-intercept and using the slope to find additional points.

Slope

The slope of a line measures its steepness and direction, calculated as the change in y (rise) over the change in x (run). A slope of 0 indicates a horizontal line, meaning that the y-value remains constant regardless of the x-value. This concept is crucial for graphing lines, as it determines how the line behaves as you move along the x-axis.

Plotting Points

Plotting points on a graph involves marking coordinates (x, y) on a Cartesian plane. To graph a line, you typically need at least two points. By using the given point and the slope, you can calculate additional points to accurately represent the line. This skill is essential for visualizing linear relationships and understanding how changes in x affect y.