The graph of the equation y = 34x + 12 is a straight line with a much steeper slope compared to the graph of y = x.
First, let’s break down both equations:
- y = x: This is a simple linear equation where the slope is 1. This means for every unit increase in x, y also increases by the same amount. The line passes through the origin (0,0) and rises at a 45-degree angle.
- y = 34x + 12: Here, the slope is 34. This indicates that for every unit increase in x, y increases by 34 units. The graph of this equation will be much steeper than y = x. Moreover, the +12 means that the line will intersect the y-axis at the point (0,12).
When you compare the two graphs:
- The graph of y = x is less steep, making it more gradual.
- The graph of y = 34x + 12 rises sharply and will be positioned higher due to the positive y-intercept of 12.
In essence, while both graphs are straight lines with positive slopes, the line represented by y = 34x + 12 rises much faster and starts higher on the y-axis than the line represented by y = x.