Final answer:
The equation of the line that passes through the given points is y = -1.5x + 6, where -1.5 is the slope calculated from two points on the line, and 6 is the y-intercept where the line crosses the y-axis.
Step-by-step explanation:
You are looking to find the equation of a line that passes through a set of points. For a line, the equation can generally be written in the slope-intercept form, which is y = mx + b, where m represents the slope and b represents the y-intercept. To determine the slope (m) of the line, you can use the formula m = (Y2 - Y1) / (X2 - X1).
In this case, using any two points on the line, for example, (0,6) and (4,0), the slope would be calculated as (0 - 6) / (4 - 0) = -6/4 = -1.5. The y-intercept (b) can be seen directly from the point where the line crosses the y-axis. Here, when x=0, y=6, so b is 6. Therefore, the equation for the line is y = -1.5x + 6.