Final answer:
To graph y = 3x - 4, plot the y-intercept at (0, -4) and use the slope of 3 to find additional points. After translating the graph of y = -4 up by 5 units, the equation becomes y = 1. The original graph has a slope of 3, while the translated image has a slope of 0.
Step-by-step explanation:
To graph the equation y = 3x - 4, start by identifying the slope (m) and the y-intercept (b). Here, the slope m = 3 and the y-intercept b = -4. This means that the line rises 3 units for every 1 unit it goes to the right, and it crosses the y-axis at -4. To graph this, you would plot the point (0, -4) on the y-axis and use the slope to find other points, drawing a straight line through them.
Next, to translate the graph of y = -4 up 5 units, you would add 5 to the y-coordinate of every point on the graph of y = -4. The equation of the resulting graph would be y = -4 + 5, which simplifies to y = 1. This is a horizontal line 1 unit above the x-axis.
Comparing the slopes of the original graph and its image, the slope of the original graph, y = 3x - 4, is 3. The image after translation, y = 1, has a slope of 0 because it is a horizontal line. Therefore, the two slopes are different, with one being positive and the other being zero.