Final answer:
To sketch the graph of a linear function passing through the points (-2, 3) and (-2, -1), we connect these two points with a straight line. The slope of the line is undefined and the y-intercept is (0, 3).
Step-by-step explanation:
To sketch the graph of a linear function passing through the points (-2, 3) and (-2, -1), we connect these two points with a straight line. Since the x-coordinates are the same, the line is vertical and parallel to the y-axis. This means that for any x-value, the y-value will be either 3 or -1, depending on the x-coordinate.
The slope of the line can be calculated using the formula: slope = (change in y)/(change in x). Since the x-coordinates are the same, the change in x is 0. Therefore, the slope is undefined.
Since the line is vertical, it does not intersect the x-axis. However, the y-intercept can be determined by looking at the y-coordinate when x=0, which in this case is 3. Therefore, the y-intercept is (0, 3).