Final answer:
To graph a line with a slope of -3 containing the point (4,-2), plot the point, then move down and right according to the slope, and draw the line through the points.
Step-by-step explanation:
Graphing a Line with Given Slope and Point
To graph a line with a slope of -3 that contains the point (4,-2), you start by plotting the point (4, -2) on the coordinate system. Since the slope is -3, it signifies a fall of 3 units in the vertical direction (y) for every 1 unit increase in the horizontal direction (x). To draw the line, from the point (4, -2), move down 3 units and then 1 unit to the right; this new point is (5, -5). Connect these two points with a straight line. This line extends infinitely in both directions, with the same constant slope throughout, always decreasing by 3 vertically for every 1 unit increase in x.
For illustration purposes, it is similar to the line graph in Figure A1 Slope and the Algebra of Straight Lines, which has a positive slope of 3, unlike our graph which has a negative slope of -3. Remember, the slope is consistent along the entire length of a straight line.