Final answer:
In Mathematics, to graph a line from a point using its slope, start at the given point and move according to the rise over run indicated by the slope. For the equation y - 4 = 3/4 (x + 2), the correct movement from point (-2, 4) is up 3 units and right 4 units, reflecting a slope of 3/4.
Step-by-step explanation:
The subject of the question is Mathematics, specifically focusing on equation graphing techniques and the concept of slope in algebra. To graph a linear equation starting from a given point, you use the slope, which is the ratio of the vertical change (rise) to the horizontal change (run). You start at the given point and move according to the slope. However, it's important to note that the given equation, y - 4 = 3/4 (x + 2), has a slope of 3/4, which means for a positive slope, you would move up 3 units and right 4 units from any point on the line.
For the provided examples, option a is correct: starting at point (-2, 4) and moving up 3 units and right 4 units would correctly use the slope 3/4. The other options describe movements that do not correspond to the slope given in the equation and would therefore not correctly graph the line described by the equation.