Final answer:
Both equations given represent the same linear equation, y = (2/5)x - 1, which is a line with a slope of 2/5 and a y-intercept of -1 on the xy-plane.
Step-by-step explanation:
The two equations given in the question describe linear equations in a two-dimensional space, commonly plotted on an xy-plane. The first equation is 6x - 15y = 15, which can be rearranged to y = (6/15)x - 1, or simplified to y = (2/5)x - 1. This equation represents a straight line with a slope of 2/5 and a y-intercept of -1. The second equation, represented as y = (2/5)x - 1, is essentially the same as the first one after simplification, meaning they represent the same line.
When graphing these equations, we look for points at which the line crosses the x-axis (x-intercepts) and y-axis (y-intercepts). To find additional points to plot, one can choose different values for x and calculate the corresponding y values. This process helps in drawing an accurate representation of the line on the graph. Remember that a positive slope indicates that as x increases, y also increases, and for a given linear equation, any two points on the line can be used to find the slope by calculating the change in y over the change in x.